So, now after 60+ years out of school I can finally calculate square roots mentally.
@ryangauthier39573 жыл бұрын
never too late to learn! that is what i love about the maths - i just learned a shortcut on subtracting fractions from a 2nd grader the other day!
@CTGReviews3 жыл бұрын
Wait, you’re that old?
@tabhorian3 жыл бұрын
@@CTGReviews Yeah, but what's the square root of that?
@want-diversecontent38873 жыл бұрын
@@ryangauthier3957 What is it? Cross multiplication?
@ryangauthier39573 жыл бұрын
@@want-diversecontent3887 actually it was subtracting mixed numbers... stack them up like a normal subtraction problem and "borrow" a whole fraction from the ones column in order to help subtract a larger fraction on the bottom. i was used/trained to find a common denom and turn them both into improper fractions, subtract the numerators and convert the answer back into a mixed number... this was kinda mind blowing to me after a couple decades of practice one way!
@mabimabi2123 жыл бұрын
This guy is like the backdoor dealer of mathematics
@rihannasahib063 жыл бұрын
FR LMFAOOO
@neelparmar66903 жыл бұрын
Yo kid, you want some roots?
@gamistry29473 жыл бұрын
@@neelparmar6690 oOhHhH i WoUlD lIkE sOmE rOoOoOtSsSs
@gamistry29473 жыл бұрын
@TIV67 Playz ?????
@josephlugo48023 жыл бұрын
Lol, that was a hilariously mathematical comment.
@grahammustoe6260 Жыл бұрын
The trick is actually based in calculus. It’s the Taylor series approximation using two terms for the square root function. Without reading through the hundreds of comments already made I’m sure several other people have probably mentioned this. Just shows you that calculus can be really useful! What’s really neat is that if you use a Taylor series approximation with three terms, its even closer to the exact value of the square root.
@bruhh489 Жыл бұрын
how would you do it with three terms?
@ncpolley Жыл бұрын
Tell us the three term trick. Wasn't able to take calc in high school.
@alexissliwak9716 Жыл бұрын
It just finds the slope of y = sqrt(x) at the perfect square, then does a y = mx + b using that slope. I'm not sure how this is using a Taylor series
@TFWPLSSUB Жыл бұрын
Taylor series of 3 terms: f(a)+f'(a)/1!(x-a)+f''(a)/2!(x-a)^2 f(a)=a^(1/2) f'(a)=1/2a^(-1/2)=1/(2√a) (the 1st derivative, which is the slope at point a) f''(a)=-1/4a^(-3/2)=-1/(4√a^3) (the 2nd derivative, which is slope of the slope at point a) x is the point you want to find, and a is the closest number (or any number, but the accuracy won't be the same) Then you have to expand it and find the cube then bla bla bla congratulations you're accurate for maybe the 3rd digit but we will round the first digit anyways
@sagaxwiki Жыл бұрын
@@ncpolley Basically the trick in this video is sqrt(x^2 + y) is approximately equal to x + y/(2*x). The original square root can be rewritten to be x * sqrt(1 + y/x^2). The Taylor series for something in the form sqrt(1 + z) is 1 + z/2 - z^2/8 + z^3/16 +... Using that Taylor series, the 3 term approximation would be x + y/(2*x) - y^2/(8*x^3) which is a little rough for mental math but doable. The easier way to improve the accuracy would be to use the closest square (rather than the square below) since y in the original square root can be negative or positive, and the accuracy of the Taylor series approximation is better the smaller the "z" term is.
@kessadecleene2 жыл бұрын
Honestly I stumbled across this while I was half drunk.😂😂 And I was somehow able to follow along and get them all right! I even kept the sheet to prove I get it! This taught me better than school did! Props to you mate! This is awesome!! I hated math but getting these answers right boosted the hell out of my confidence!!
@marriedwithchildren-familylife2 жыл бұрын
lol, me? graduated HS in 1979; never went any further than gen math. FFWD to 2006 I found myself in college earning a BCS/IT which required algebra 1&2 and Geometry; needless to say I did not do so well with sqrt's ;) FFWD-again, to tonight and I find this video while having drank 1/2 bottle of 10 year old single malt Irish whiskey in celebration of my 61st birthday.... WHAM! 'I now can do sqrt's in my head! I'm not fast (yet). Thanks, just doesn't cut it.
@thereforeayam2 жыл бұрын
@@marriedwithchildren-familylife the square root of half a bottle proves the Irish reverse-discovered North America
@thesomething-er1025 Жыл бұрын
Yea i looked at this at 10 pm and followed along fully, this guys a legend!
@dredwick Жыл бұрын
Are you laughing at yourself for being half drunk and scrolling through KZfaq to watch math videos? Fckng boring af bro
@memirandawong Жыл бұрын
I used to have a shot of Scotch before every calculus test! LOL
@miabasile60043 жыл бұрын
"I'll give you acouple seconds to work that out" Me: Sweating A 30 second add: "I got you"
@tryfan47053 жыл бұрын
@TIV67 Playz dafuq
@atos_alivetoscare_53903 жыл бұрын
@TIV67 Playz Amen... B-Men, C-Men... X-Men
@tryfan47053 жыл бұрын
If jesus can walk on water can he swim on land
@atos_alivetoscare_53903 жыл бұрын
Demon too, I must say.
@c4g3dB34st3 жыл бұрын
@TIV67 Playz well and good, will it work on how to find square root?
@Smallpriest2 жыл бұрын
How engineers find square roots instantly: Step 1: find the closest perfect square Done
@finnrock55582 жыл бұрын
As an engineer I can say that it's either this or "Ok, someone boot up MATLAB"
@Consul992 жыл бұрын
@@finnrock5558 personally I prefer to use simple tools such as calculators and physicists.
@finnrock55582 жыл бұрын
@@Consul99 ah yes, physicists. The best tools
@bouipozz2 жыл бұрын
@@finnrock5558 @Herp Derp You two must work for good companies, we're not allowed to claim for physicists.
@fortnite-kq7ok2 жыл бұрын
I love this level of humor
@parisgreen4600 Жыл бұрын
This is great! I always thought I was 'bad at math' until I took a VERY basic course in my 40s and discovered that, not only can I do math well enough to get by, but it's actually fun. Your video presentation is super clear and friendly. I was able to do all the problems the first time through; going to check out your other videos now. Thank you!
@podcastsio9 ай бұрын
Can u give link for that course
@peachycloudz6438 Жыл бұрын
This is actually perfect for me, I recently learned about square roots this year and this will be very useful for the years to come. Thank you
@moochington3 жыл бұрын
Never expected Bruce from Finding Nemo to be teaching me math tricks at 3am yet here I am
@sirhawkjames3 жыл бұрын
3:38am right now for me too lmao
@muhammadtroll28353 жыл бұрын
4:09 AM
@mohammadyousif15063 жыл бұрын
@@muhammadtroll2835 yo another Muhammad
@DestinyatTube3 жыл бұрын
Can you explain me...i don't get it.
@mohammadyousif15063 жыл бұрын
@@DestinyatTube same voice
@MineSweeper-bg8un3 жыл бұрын
I can't believe how much an 8 minute video expanded my brain by
@barbozafernandezclaudioema15853 жыл бұрын
Lmao
@greatmnn38683 жыл бұрын
It came from Binomial theorem.... It is Approximation of infinite series.....
@duk82273 жыл бұрын
Lol. I mean its only useful for lower grades like grade 8 because in higher grades u would prob need more exact numbers
@greatmnn38683 жыл бұрын
@@duk8227 bro, its from Binomial Theorem .... If at higher level you need more digits... Them Expand it more and more..... Its infinite series....... You can get whatever amt u need...
@MrTrollo23 жыл бұрын
@@greatmnn3868 u can just type in a calculator and get the correct result. The trick might be interesting in some cases to get the first decimal number but if you are able to estimate the root by taking the root of the next smaller quadratic number you have a reasonable estimation already. In other words, this is useless on any level.
@ernjdasdd2 жыл бұрын
Well to be technical, the square root would be much easier when comparing the remainder number to the next closest perfect square. So 36 squared is 6, but we have 3 left over from the 39, the next closest square is 49, the difference betwen 36 and 49 is 13, so we have our remainder over the difference. The square root of 39 is 6 and 3/13ths.
@7SeventhFromAdam2 жыл бұрын
I was never really good at math. Learning this method actually piqued my interest with numbers. I enjoyed the challenge. Thank you!
@Birju_Maharaj5 жыл бұрын
Note : this trick is actually quite good in competitive exams where approximations work,,, thanks
@kankanmalakar4 жыл бұрын
BHAI BANKING ASPIRANT HAI KYA?
@Birju_Maharaj4 жыл бұрын
@@kankanmalakar no bro
@Birju_Maharaj4 жыл бұрын
@Ronak Bhadarka anywhere where calculator isn't allowed
@mikatu4 жыл бұрын
maybe in your exams.... in mine, you really had to give the correct answer. Ah, but I am from a developed country, not from india....
@Birju_Maharaj4 жыл бұрын
@@mikatu and that's why u don't know the jugaad technology we use for the optimum utilisation of the resources available to us😉
@u8f72 жыл бұрын
Here's how this works algebraically: Let √c = a + b, where a represents the whole number component of the answer, a ∈ Z, and b represents the decimal component, 0 < b < 1 c = (a + b)² c = a² + 2ab + b² Now solve for b: 2ab = c - a² - b² b = (c - a² - b²)/2a b² (the decimal component squared) will be very small, so we can ignore it therefore, b ≈ (c - a²)/2a in other words, b ≈ the original number, c, minus the nearest perfect square below it (the whole number component squared), all over 2a: which is the formula given in the video for working out the non-whole number part of the answer e.g. √27 = 5 +b 27 = (5 + b)² 27 = 25 + 10b + b² 10b = 27 - 25 - b² b = (27 - 25 - b²)/10 b ≈ (27 - 25)/10 b ≈ 0.2 √27 ≈ 5 + 0.2 = 5.2 As further proof, the approximate answer will always be out from the actual answer by a margin of b²/2a: 5.2 - 5.196... = (0.196...)²/10
@felipearrais54152 жыл бұрын
Should have more likes. Thanks for the explanation.
@mr.niceguy17062 жыл бұрын
My brain has not developed that kind of math yet
@toren14262 жыл бұрын
woah! that’s interesting, but i sure don’t care!
@raehaa33432 жыл бұрын
*sweats tears*
@Joe_Mama.also_YTHandlessuckass2 жыл бұрын
So simple
@wild_lee_coyote Жыл бұрын
Reminds me of Richard Feynman when an abacus salesman challenged him to a math contest. Ended in a square root contest. Feynman won because the number was close to a perfect square and he could quickly refine the number. That and doing square roots on an abacus is very labor intensive.
@dougdimmedome55522 жыл бұрын
I never knew that being taught math by an Australian was something I needed in my life.
@publiusii42462 жыл бұрын
This is actually impressively precise. For my own enjoyment I wrote a script that used this method for the root of every number up to a million. The highest margin of error was a little over a fifth for the root of three. With precision trending to increase proportional to the size of the number. By the time you reach thirty the number is accurate to +/-0.1
@brma31242 жыл бұрын
Did this method ever guess low? Seemed like all the examples in the video slightly overestimated the true value.
@WhatsAGoodName420692 жыл бұрын
It gets better if you adjust it a but, if the number is closer to the next highest square rather than the previous lower square. You use that higher square and subtract much like he adds. So 34 would be 6 - 2/12 = 5.83. But who wants to do subtraction, amirite
@publiusii42462 жыл бұрын
@@WhatsAGoodName42069 I noticed that as well and came to the same conclusion. Considering I was happy with the root of 87 is nine and a bit before this video. I'll take accurate to a tenth and not do subtraction.
@Geweldenaar2 жыл бұрын
But if you got a really big number like 938993 how do you know what the nearest whole square root number is
@publiusii42462 жыл бұрын
@@Geweldenaar that's memorization my friend. Personally I only know up to 20squared off the dome. And that's fine by me I give up on mental arithmetic in the mid 3 digits anyway.
@JulianShagworthy2 жыл бұрын
This can be improved slightly by choosing the CLOSEST perfect square as opposed to just picking the one below. For the sqrt 138 example, choose 12^2 = 144, then SUBTRACT 6/24 (which is the same as 1/4) from 12, leaving 11.75 as the answer, which is closer than the 11.77 obtained using the original method.
@palman84802 жыл бұрын
Thank you I'll remember this
@colehindes62352 жыл бұрын
Yeah it can be done for any power if you subtract your real number from the nearest perfect and take the derivative of the constant where the number is x and adding that to the perfect power
@colehindes62352 жыл бұрын
I’m sorry that sounded very confusing pretty much f(x)+f’(x)(a-x)
@Compucles2 жыл бұрын
It also gets improved just by adding 1 (or subtracting 1 if calculating from the perfect square above) to the denominators, such that sqrt(138) = about 11 & 17/23, which is about 11.739 (compared to the real answer of about 11.747). It works better this way, since (n+1)^2 - n^2 = 2n + 1 (or in this case, 12^2 - 11^2 = 11*2+1 or 144 - 121 = 23) rather than 2n.
@ronnymcpherson46092 жыл бұрын
Thanks!
@Gartenpunkt Жыл бұрын
Also interesting: If you accidentally pick the wrong perfect square, it still kind of works... Sqrt(155) Based on 12^2=144, with a difference of 11, gives 12+11/24 = 12.4853 Based on 11^2=121, with a difference of 24, gives 11+24/22 = 12.0909 Correct answer would be 12.4499. This error self correction works better the higher the number you're taking the square root of.
@KpC169 Жыл бұрын
I think it works better the closer the perfect square is to the number
@SouL-ob5wx Жыл бұрын
Wouldn't the difference between 121 and 155 be 34 and not 24? In which case it would be 11 + 34/22 which is approx. 12.54
@user-wi3nd9gx9d Жыл бұрын
This is true because this trick should be fine as long as your difference is less than the perfect square you're using to approximate.
@Klonion_009 Жыл бұрын
Wow I just learned more in ten minutes from youtube than I learn in algebra 1 honors in an entire week
@-Minuano-2 жыл бұрын
Math is fun when your “life” doesn’t depend on it. Aka grades. Edit: 13k likes!? Holy... Thank you, everyone. Also, there's a fight in the comment section lmfao. I'm very sorry I caused this chaos.
@alexanderkaiser892 жыл бұрын
Grades is fun. They motivate you to discipline yourself into the mentality to work hard and eventually success and master it.
@lordkhan2 жыл бұрын
Good for people who can't motivate themselves without them, I guess.
@SapphireeCos2 жыл бұрын
@@alexanderkaiser89 you get judged with grades your entire life, it's hard to keep focusing always giving your best.
@alexanderkaiser892 жыл бұрын
@@SapphireeCos As I’ve been taught and what I have researched on my own in this very topic, it firmly depends on discipline and willpower. I’ve you’re being judged by your grades, it is partially up to you, to change that very situation and your surroundings.
@Finmide2 жыл бұрын
idk man it's still not fun for me even after school and not needing to worry about grades. After all I really only use the stuff from grade school in my day to day.
@MalarkeyMan4 жыл бұрын
Why does this get recommended the day after my test
@Ray-td4gk4 жыл бұрын
And why does this get recommended on day when my friend said this is magic and i will never get it on internet
@sweetygupta9724 жыл бұрын
Badluck I guess ?.....
@Anonymous-zd1ow4 жыл бұрын
This is KZfaq's idea of a joke.
@MalarkeyMan4 жыл бұрын
0g1f I want to pass the test
@NROS20124 жыл бұрын
Because you were probably talking a lot about your test near your phone/ Siri / Alexa or texting or messaging about it. Your phone and apps listen to you and analyse your messages and then adverts and marketing appear to suit what your talking about.
@Raging.Geekazoid Жыл бұрын
The nearest perfect square you start with doesn't have to be smaller than the target number. If it's larger, all you need to do is subtract instead of adding. So the square root of 80 comes out to 9 - 1/18 = 9 - .05556 = 8.94444, compared to the exact value of about 8.94427, or 8 + 16/16 = 9.00000.* *(was 8 + 6/16 = 8.375 before correction)
@Olibaby12 Жыл бұрын
You made a mistake in the last part, it would be 8 + 16/16, which is 9. That is because sqrt(64) = 8 80-64 = 16 8*2 =16 Thus 8 + 16/16 = 9
@Raging.Geekazoid Жыл бұрын
@@Olibaby12 Well I'll be darned! Thank you. 🙂
@sofusflorjensen36892 жыл бұрын
On the one with the square root of 138, I actually tried using 12 instead of 11, giving me the number 144. Here I subtracted the 6 and divided it with the 12 doubled, 24, boiling down to 0,25. But since I am under the actual value instead of over, I simply subtract the 0,25 from my root 12 instead of adding it on top, as he does with 11 in the video. Hope this made sense, and might help someone, have a nice day if you find this
@AaraBeloved Жыл бұрын
Yea, using the value (square) *closest* to the number (the one we're finding the root for) proves less error than always going for the one below. Especially since, fractions with larger numbers that don't share common factors will have the most inaccuracy. Instead of 11 + 17/22 (= 11.77~) your more accurate answer would be 12 - 6/24 = 12 - 1/4 (= 11.75). Because 138 (the number we want to find the root of) has a larger difference between 11^2 than 12^2 (138 - 121 = 17 but 138 - 144 = 6). Ty for opening a discussion towards using values higher than the simply lower ones for every situation.
@zaccandels66954 жыл бұрын
For anyone who's curious: This is based on a linear Taylor Series approximation of the square root function. For example- Sqrt(x + dx) ~ sqrt (x) + (1/2)(dx)(1/sqrt(x)) And this is exactly what he's doing
@absxn3 жыл бұрын
neat
@aSeaofTroubles3 жыл бұрын
There is also an elementary reason for this, for non-calculus students.
@gardening_vibes3 жыл бұрын
@@aSeaofTroubles then tell about it please
@iRaT553 жыл бұрын
@@JonathanBartlesSWBGaming the formula in the video comes out from the taylor series with an error of the first degree. So they are using the same way to calculate it.
@johngreen35433 жыл бұрын
Thank you, for doing this. It saves me the trouble.
@elormavevor65046 жыл бұрын
If anyone wants to know how this works, it essentially uses the fact (x+a)² = x²+2ax+a² For example, √(37) is a little more than 6 so call that little extra bit a Then √(37) = 6+a Squaring both sides gets 37 = 36 + 12a + a² 1 = 12a + a² Since a is small, a² is small and can be ignored thus a ≈ 1/12 so √(37) ≈ 6+1/12 Approximations are better when a is smallest (the number being rooted is large and close to a perfect square)
@elormavevor65046 жыл бұрын
You can get better approximations by then saying √(37) = (73/12 + a) and repeating the process
@evanwalsh41735 жыл бұрын
You guys are nerds
@undertraper5 жыл бұрын
Watching the video at 2am, couldnt sleep bc the interest was carving inside of me, thnks for saving my sleep.
@lexsi6935 жыл бұрын
@@undertraper same. here its now 3am ^^"
@katiekat18435 жыл бұрын
i dont understand...cause im still in elementry school...
@RWBHere6 күн бұрын
As a rule of thumb, it's always worth remembering that any half digit squared is the multiple of that digit times that digit plus 1, and add a quarter. It's simpler mental arithmetic: So 3.5² is ((3x4) + 0.25) = 12.25. Therefore, for your example of sqrt(12) the answer has to be a little less than 3.5, or roughly 3.45. Similarly, 11.5² = ((12x11) + 0.25) = 132.25. And 100.5² = ((100x101)+0.25) = 10,100.25. Even 0.5² works: ((0x1) +0.25) = 0.25 These shortcuts are often very useful to know when calculating square roots of nearby numbers.
@dial4655 Жыл бұрын
This is just a special case of the formula (aⁿ+f)^(1/n)=a+f/naⁿ-¹, where a, f, n are integers. And also √(a²+f)≤a+f/2a (only for n=2).
@user-fy4ur5im4q3 жыл бұрын
I trust this man with my life.
@tryfan47053 жыл бұрын
@TIV67 Playz no
@noahr.hopkins28003 жыл бұрын
@TIV67 Playz Jesus is coming indeed bro!
@CH-yt6qi3 жыл бұрын
Ooof…I misread that you trust this man with your wife…
@Sidguru1013 жыл бұрын
@@CH-yt6qi same 🤡🤒
@whenly66903 жыл бұрын
@TIV67 Playz these guys are getting annoying
@AndreLuiz-lm9iz3 жыл бұрын
He did not tell you that in the video, but in case the sqrt is closest to a full number higher than itself, you should use that instead, and your second part of the answer (that comes after the point) will be negative. You'll do the division normally, and then subtract from the big number (i.e. closest full number that stays in front) and you'll get your answer. Example: sqrt of 24, you'll go for 25, and the subtraction will lead to 5 -1/10, which is 4.90. The actual answer is 4.89
@vyomagrawal41412 жыл бұрын
Thanks
@mike_slav04772 жыл бұрын
no the answer actually is 4.9 when you round it up
@AndreLuiz-lm9iz2 жыл бұрын
@@mike_slav0477 the point of this method is that it's a simpler version of an approximation equation. You'll never get the exact same number unless you round it up. I simply wanted to show that you should use the closer number even if it's a higher one. If you were to use ✓16 it wouldn't work. That's all there is to it
@najwaalmira35662 жыл бұрын
thanks lov
@finisher95052 жыл бұрын
Thank you a lot
@Food4Cats Жыл бұрын
There's one more similar way, for example for √ 127. You could get the smallest closest square which is √ 121 and the biggest closest square which is √ 144, then subtract the smallest square's number from the biggest square's number, so 144-121 = 23, get how many numbers there are from the smallest root to the root we're trying to calculate: so 127-121 = 6, and then the answer is √ 121 + 6/23 = 11.23 (Closest smallest square + digits from smallest square to the square we want to calculate/numbers in between smallest square and biggest square)
@grahammustoe6260 Жыл бұрын
For anyone who is curious as to why this works, this method is employs linear interpolation, or the principle of similar triangles.
@JerkleCirc Жыл бұрын
I've been doing this since freshman year of high school and never really had someone show me the process. My head just used to do it. I don't know what fascinated me about square roots, but it started in 8th grade geometry. I wanted to find the relationship between two squares, so I made it an equation. If a + 1 = b, then a^2+(2b - 1) = b^2. I tried to show my teacher, but got no encouragement. So I kind of kept all that nerdiness tucked away. But it led to an obsession with physics, which gave me something to talk about when I met the cousin I didn't know we had. Turns out, when we met her, she was working at LIGO in Louisiana and is one of the many scientists credited with the discovery of gravitational waves! So, all in all, ended up not feeling like I needed to suppress it anymore, even if my friends are weirded out by it sometimes.
@nicoletion17293 жыл бұрын
the way this came out 3 hours before my scholarship exam starts thank you
@safwanshahriar41083 жыл бұрын
U should thank the youtube algorithm.
@prashantsinha67813 жыл бұрын
@@safwanshahriar4108 yeah. lol
@sseblante3 жыл бұрын
Hey, how'd it go?
@nicoletion17293 жыл бұрын
@@sseblante it went great! i actually passed and now im a scholar! 👍
@kamranahmad66783 жыл бұрын
@@nicoletion1729 Congratulations 😁
@Kiiohru3 жыл бұрын
This is a good place to get my brain cells back after seeing tiktoks
@somakiran32633 жыл бұрын
LmaoXD
@Nerbto2 жыл бұрын
Just took a devious lick of knowledge 😜
@mo-vz2xk2 жыл бұрын
@@Nerbto cringe tiktok 0 braincells user
@Nerbto2 жыл бұрын
@@mo-vz2xk thank you
@Sean-dl4fh2 жыл бұрын
@@Nerbto I have never felt more disgusted just by reading words
@maximus5ss5 Жыл бұрын
Well, that's a specific case of approximate calculation using the differential (here and further AC w/d) for square roots. The idea is to use the fact that f(x)=f(x₀+Δx)=f(x₀)+Δf(x) As differential is approximately equal to function change (dy~Δy) we have f(x)~f(x₀)+df(x)~f(x₀)+f'(x₀)Δx For √x prime is 1/2√x, that's why we multiply the whole part by 2 before putting it into denominator: f(√(x₀+Δx))~f(√x₀)+(1/2√x₀)×Δx~f(√x₀)+Δx/2√x₀ Couple of examples from video: √87=√(81+6)~√81+6/2√81~9+6/18~9.(3) √39=√(36+3)~√36+3/2√36~6+3/12~6.25 √138=√(144-6)=√(144+(-6))~√144+(-6/2√144)~12-6/24~11.75 (Here it's been seen that it's possible to take any comfortable value, but then Δx can be negative as in AC w/d there is not a "±" sign but a "+" one) But, being honest, the "rule" mentioned here, though works only with square roots, is easier to remember than AC w/d
@motaparatu Жыл бұрын
I tried this on a few numbers and checked them with a calculator. Pretty darn close. It's kinda like using 22/7 for pi. I'm impressed.
@AdamKlownzinger2 жыл бұрын
Actually said “YOOOO” and had to walk around for a second because the math hit too good LMAO
@rudecrok47342 жыл бұрын
WTF SAME
@crimsonneko2 жыл бұрын
I guess it works for people who can convert fractions into decimals in an instant, but since I am not one of those people, this method doesn't help me too much.
@BingQiLing.2 жыл бұрын
@@crimsonneko fractions to percentage is harder
@crimsonneko2 жыл бұрын
@@BingQiLing. not really. Once you have the decimal you just move the decimal place 2 times to the right and then you have your percent.
@loganrhill3 жыл бұрын
Alternate title: Thor teaches you how to solve square roots :)
@alexthealex74923 жыл бұрын
BRUH I DIDN'T NOTICE TILL NOW
@alexthealex74923 жыл бұрын
@TIV67 Playz Does Jesus love Gidon?
@someone_29283 жыл бұрын
@TIV67 Playz amen
@extestential66383 жыл бұрын
Hes austrailan tho
@halfbloodbrit25183 жыл бұрын
@@extestential6638 One clearly does not understand what a joke is
@jonghyeonlee5877 Жыл бұрын
For those who want an explanation that doesn't require things like "Taylor Series" which you may not be familiar with: 1. Consider the following expression: (a + b)^2 = (a^2 + 2*ab + b^2). 2. You can run this in reverse to find the square root of anything by treating it as (a^2 + 2*ab + b^2), then finding what a & b are, then finding what (a + b) is. 3. To make this easier, you can round b^2 to 0 because if you do it right, it's pretty close to 0. 4. You can now think of any number as (a^2 + 2*ab) = (a + b)^2. 5. To find a^2 and thus a, think of the perfect square just below your number, and remember its square root, as the video says. E.g. 87 has the perfect square 81 not too far below it, which is the square of 9. In this example, a = 9. 6. Now find the remainder & work out what b would have to be. 7. In this case, the remainder is 6, which has to be 2*ab. Find b by diving 6 by 2*a, or 2*9, or 18. 8. The square root of 87 therefore is about 9 + 6/18, or 9 and 1/3. 9. And it all comes from an approach you can independently rederive yourself, just by remembering that (a + b)^2 = something & then reversing that something with an approximation. If you ever forget this exact method, know that you can rediscover it yourself. 10. Hope that was helpful. (11. If you're curious, the thing people in the comments are saying about sometimes taking the *higher* perfect square instead of lower perfect square, comes from using (a - b)^2 = (a^2 - 2*ab - b^2) ≈ (a^2 - 2*ab) instead. It gets closer results if the higher perfect square is closer than the lower perfect square.)
@dreamsolutions3037 Жыл бұрын
I did these all by guessing, based on intuition, about how far the remainder was between the 2 perfect squares and I was surprised to find that my guess was never more than .05 away from the correct answer. You're technique was much closer, but I think I'll stick to my intuition since I don't have to think.
@finnrock55582 жыл бұрын
I made a quick excel spreadsheet and graphed the percent errors of this method. The %error curve is a sawtooth pattern, but the peaks look to be decaying exponentially. This is very interesting, thanks for sharing.
@Blitztein_beta2 жыл бұрын
-Can you show us an image of the graph?-
@baked_beanz05222 жыл бұрын
@@Blitztein_beta how would they do that 🤣
@TheMrk7902 жыл бұрын
Yeah its because the taylor series is just the sum of the derivatives devided by the faculty of the index (nth derivative/n!). As we are only using the first summand of that series, the rest of the series is our error. Now this sum for the sqrt of x looks like an exponential of 1/x, if you look at the series formulation of exp. Thus you get the exponential decrease in the peaks. P.S. thought about it again. It is just wrong.
@pato15412 жыл бұрын
@@TheMrk790 you know what's insane, anyone that understood what you said knows you're just bloviating and anyone who doesn't, doesn't care about what you're saying.
@Nuisance_Bear2 жыл бұрын
@@pato1541 what if you’re too dumb to know what he’s saying but still smart enough to know he’s just stroking his own ego
@Strangevil5 жыл бұрын
it's difficult to find the nearest perfect square if the number is very large.
@Minecraftgnom5 жыл бұрын
But only needing to know a nearby square to estimate a root can really help at times. :D
@DonVigaDeFierro4 жыл бұрын
It's difficult to do any operation when numbers are very large.
@redsgxd4 жыл бұрын
Its difficult to find larger numbers but its closer the larger you go.
@Fritzafella4 жыл бұрын
@@redsgxd Esitmating the sqrt of something large is still still relativly easy using this method, your error just gets bigger. Just Divide your number by 100 until it is smaller than 100. ex 32767=100*100*3.2767 sqrt using the above method (That I will modefy slightly for increased accuracy) 4 (closest square) -3.2767= .7233 so you get 2-(.7233/((2-1)*2))=1.819 then cuz we divided by 100 (or 10^2) twice multiply back by 10*10 and your final answer is 181.9 sqrt(32767) is exactly 181.1..... so still reasonably accurate
@soulswordobrigadosegostar4 жыл бұрын
That's the disadvantage of it,it kind of breaks with bigger numbers
@Tanayxx23 күн бұрын
Im so glad i saved this, i learned square roots just this week and i think this will be really helpful in the coming time
@rashidissa5887 Жыл бұрын
When I read the comments, which are generally in praise and appreciations,then I feel not left behind. I simply ended up with 'O' Level maths but for the love of it I am still following lessons in U-TUBE. I am 78 now
@kaydonmartin17372 жыл бұрын
It is also possible to start with the closest square root above and subtract the fraction as shown. Example root138 = 12 - (6/24). Root 138 = 11.75. Good luck!
@AntonioNoack2 жыл бұрын
you can also apply this same step to your won approximation. It will be a littler harder to calculate, but it will improve your results :) e.g. use 138-11.75², and then 11.75 + difference / (2*11.75) Because it's Newtons Method, and you can use as many iterations, as you like :)
@GahloWake2 жыл бұрын
I wonder if it becomes more accurate to do it to the closest suqare, since in that example you were spot on while the video was off by 0.02.
@rtyk12 жыл бұрын
@@GahloWake Yes, it would be more accurate to do it to the closest square. How the trick works is it uses the common school formula (a+b)^2 = a^2+2ab+b^2, sets a as the lower perfect square so that 0 < b < 1, and then assumes that b^2 is small enough to ignore. If you go to the closest square (sometimes above), what you are doing is reducing the size of b^2, in other words reducing the error of the trick
@acoolcat42692 жыл бұрын
@@AntonioNoack use normal english. im mere mortal i do not speak the language of the gods.
@shubhgulati2 жыл бұрын
This actually makes the trick more accurate, trying for root 15 by the addition method will give 4, but the subtraction method you suggested (essentially follow the closest perfect square and do accordingly) gave 3.875, which is very very close.
@Kangakool3 жыл бұрын
Why didn’t I get taught this in school? They ask about estimating square roots on the gre and other advanced tests, this would have been so helpful.
@absalon19923 жыл бұрын
Cause School doesnt teach you anything
@spoopyscaryskelebones38463 жыл бұрын
@@absalon1992 not even a little smidgy widgy?
@absalon19923 жыл бұрын
@@spoopyscaryskelebones3846 What
@yahirdoesbadvids3 жыл бұрын
@@spoopyscaryskelebones3846 nah the smidgy widgy is taught only by the ancient ones.
@eljahihamgottin45403 жыл бұрын
@@spoopyscaryskelebones3846 Smidgy Widgy is an infamous art. You think schools are going to teach that? You have to travel out to the himalayas and speak to master Wu to learn Smidgy Widgy.
@oriontaylor82202 жыл бұрын
This method is equivalent to taking a single newton step to find the root of the function f(x)=x^2 - q (or g(x)= 1- x^2/q ) where q is the number you want to find the square root of, and the initial guess x_0 is sqrt(q) rounded up or down. Since you always start within +/- 1 of the true root, the initial error g(x_0) decreases with the size of q. Combined with the quadratic convergence of Newton's method, the result is that this approximation technique gets more precise as q gets larger.
@g0t0h612 жыл бұрын
This may be old but i helped with my non calculator exam Im so happy i watched this the day before
@cursed_cats57102 жыл бұрын
I stumbled upon something similar to this a few years ago and presented my technique to the math class. Teacher was convinced enough to let us use the technique over the slower "multiply 'til you find it" method in the curriculum.
@christiantasidaily2 жыл бұрын
“Yeah, you should be able to work that out by now” *starts sweating profoundly*
@alyssa67352 жыл бұрын
Right
@mydickisunbelievablysmallb81322 жыл бұрын
*profusely
@christiantasidaily2 жыл бұрын
Na
@princekhatri88 Жыл бұрын
Bro I know many of the commenters won't believe it but right at the start of the video I stopped your video and then I used the a+b ^ 2 in this then found the same formulas of 2a division like you.
@lonko17311 ай бұрын
what Id do is for example| sqr(27) then full number from that is 5 from sqr(25) -> whats left is 2 -> the next full number would be from sqr(36) -> 2 stands around 2/11th of the way between full numbers so its 5 and 2/11 but thats always a little lower than the actual answer. And the one in this video is more precise from what I see
@TSfish942 жыл бұрын
I can’t believe how simple this is. Definitely wish I knew about this 10 years ago.
@dankmemes82542 жыл бұрын
I was stunned at how stupidly easy it is
@tropheusanims6982 жыл бұрын
Fr
@feeldog10192 жыл бұрын
Yeah but on a test basically all those decimals are wrong so you would have the wrong answer
@Bilbo1teaBaggins2 жыл бұрын
@@feeldog1019 I think it helps to see the number in a "normal" form so its easier to understand
@TSfish942 жыл бұрын
@@feeldog1019 depends on the instructor. I had a chemistry teacher that would allow you to approximate your answer if you could prove your answer was reasonable. Usually this was only on tests where calculators weren’t allowed, but it’s worth noting. Plus with this method you could trivialize multiple choice questions by going with whatever’s closest to your result.
@amitav11295 жыл бұрын
For 138, we can also do square root of 144 minus the difference/double of the √144 =12- 6/24 =12-.25 =11.75
@HritwRaje5 жыл бұрын
Square root *
@erickzaragoza12395 жыл бұрын
THX
@ucanhha49565 жыл бұрын
The smaller the difference is, the closer you get the answer
@ejay4675 жыл бұрын
Maybe even if its lesser or greater, atleast the most closest will be more accurate.
@markvincentordiz5 жыл бұрын
more closer
@tin-man56872 жыл бұрын
Dang... That's actually rather fun to do. Thanks for the tip. 👍
@mixedreamz73242 жыл бұрын
So excited to be watching this on a Saturday morning.
@herculesbeats84996 жыл бұрын
How to get answers wrong.. but CLOSE!
@MaximilianBerkmann6 жыл бұрын
From all the sqrt approximation calculations I've seen so far this one and Andrew's are the most reliable.
@paulie5B6 жыл бұрын
VF7 how to estimate without a calculator dingbat
@MaximilianBerkmann6 жыл бұрын
@nano bot27 It's called approximation.
@reznovvazileski31936 жыл бұрын
It's called aproximation. My astrophysics teacher always says: "ah well it's the same power of 10 right?". It's just a matter of how accurate you require your result to be whether you want to use this or not :P
@weinerglory6 жыл бұрын
@@paulie5B it's actually possible to calculate more accurately but you need a lot more space for paper
@josephlugo48023 жыл бұрын
This guy's like the breaking bad of mathematics. This is methmatics. lol
@interestedperson1743 жыл бұрын
i applaud you i am so proud
@e_hland2 жыл бұрын
3:33 how does its 6.25 I cant understand
@lanzhaan87672 жыл бұрын
@@e_hland i think it's 6.25 because 3/12= 0.25 and he added that to 6.
@moritz47872 жыл бұрын
@@e_hland 3 is 25% of 12 thats why bro
@moritz47872 жыл бұрын
and 25% equals 0.25
@jalalraza13132 жыл бұрын
This is an awesome trick so glad to have learned it, mental math techniques like this are too rare in modern education
@blutey2 жыл бұрын
Great. 45 years ago, a school friend could do square roots of integers in his head like this and we were always amazed, but never knew how he did it. He of course never let on on the trick. Now all is revealed!
@Tsskyx8 жыл бұрын
For smaller numbers, you can get a much better approximation if you calculate a square root of a number that's 100 bigger and then divide the result by 10, so sqrt(2) = sqrt(200)/10. This is because the higher the number is, the better the approximation will be.
@dggoldst6 жыл бұрын
Great tip deep in the comments!
@eddysetiawan23296 жыл бұрын
This should be pinned
@traveler14916 жыл бұрын
Great tip.
@MRU2be6 жыл бұрын
Yeah ! but finding the required intuitive square root of 8700 (93) is far more complicated than 87 (9). The final fraction becomes also more challenging (51 / 186). You get of course your loved 93.27 / 10 = 9.327.
@ronalddump40615 жыл бұрын
In the end, it would be far better to just take a few minutes to learn to do the real method for finding square roots to as many digits as you desire. You are not gaining anything at all by trying to learn these "tricks" What I am suggesting is that you have no business learning "tricks" to do something, until after you have actually learned a functional method to do that something.
@hasiburrahman56373 жыл бұрын
Less than 1 month remaining for my competitive exam, and i have found the channel. I'm feeling blessed
@hasiburrahman56373 жыл бұрын
@You dont know me I'm from Bangladesh, and its my undergraduate admission exam!
@ARealTaco3 жыл бұрын
@@hasiburrahman5637 how’s you do
@cheddarbob83683 жыл бұрын
@@hasiburrahman5637 how’d u do
@justlocar2 жыл бұрын
update
@nickdiaz67662 жыл бұрын
Poke update
@tethyn Жыл бұрын
It seems there is an interesting pattern of using the method with a perfect square minus 1. For instance sqrt 15 using the method is 3 6/6 which gives you 4. Sqrt 24 is 4 8/8. Sqrt 35 is 5 10/10 and sqrt 143 which is 11 22/22. To get a better approximation is to do the opposite where you start with the next perfect square and subtract the difference (another comment in the thread goes over that). Other than that the method is very useful and thank you for the video. It was engaging and I learned something new. Take care.
@thesysop4998 Жыл бұрын
thanks bro I was wondering how everybody in my class was doing square roots in their heads
Жыл бұрын
Unlikely that this is it. Maybe they just know the perfect squares
@p4scol3s4 жыл бұрын
i don’t need sleep, I need answers.
@lolzhunter4 жыл бұрын
it essentially uses the fact (x+a)² = x²+2ax+a² For example, √(37) is a little more than 6 so call that little extra bit a Then √(37) = 6+a Squaring both sides gets 37 = 36 + 12a + a² 1 = 12a + a² Since a is small, a² is small and can be ignored thus a ≈ 1/12 so √(37) ≈ 6+1/12 Approximations are better when a is smallest (the number being rooted is large and close to a perfect square) (copied off another comment)
@RajSinghTanwar_4 жыл бұрын
@@lolzhunter lol dude get a life
@magnusanderson66814 жыл бұрын
@@RajSinghTanwar_ Somehow I find it less lively to boast ignorance than to share knowledge. Might just be me though.
@RajSinghTanwar_4 жыл бұрын
@@magnusanderson6681 stfu you aint got no life so how can you boast cuz u aint got nothin to boast bout lol
@nekso37604 жыл бұрын
@@RajSinghTanwar_ Clearly, the guy mentioned that he copied the comment. I would recommend you to stop being so ignorant and a recalcitrant person as he was only helping the other person. If you're a person who can only say to other people to "go get a life" - then I say you're the one who needs to get a life. Thank you :) Note: pls spread happiness and harmony. It's not hard
@MitchBurns2 жыл бұрын
I’ve never seen this before, but it’s actually pretty easy to see what that trick is really doing mathematically. All it’s doing is converting the continuous function root(x) and converting it to a piece wise function by connecting the points at perfect squares with strait lines. It works because the inverse function of x^2 has a derivative of 2x, so the slope of each new line is 2x. It’s a pretty neat trick.
@derdreibeiner14172 жыл бұрын
Exactly...
@gameswoodmore59502 жыл бұрын
This also means that if n is the root of the next smaller perfect square the error will never exceed 1/(2n) which is really neat.
@FlipflopB2 жыл бұрын
Yeah dude I was totally thinking the same thing!
@jameyfrey74452 жыл бұрын
Can you explain why it doesn’t grab an exact number?
@gameswoodmore59502 жыл бұрын
@@jameyfrey7445 What do you mean by "grab an exact number"?
@5k_Sub_challenge_with_no_video Жыл бұрын
But you could also subtract the number with the nearest bigger perfect square no. For example, Find √8 √8 = √(4+4) ≈ 2 + 4/4 = 3 But If you try subtraction then, √8 = √(9-1) ≈ 3 - 1/6 = 2.833 And actual value of √8 is 2.82...
@ThePiMan0903 Жыл бұрын
Very nice and helpful sir! This is very useful for estimating radicals. Thanks again!
@daffy89773 жыл бұрын
I've noticed that the closer you are to a perfect square, the more accurate the answer gets. When I say closer I don't mean sqrt 2 is very accurate bc it's one away for sqrt 1, I mean fraction wise of the number, 2 to 1 is a big jump of 1/2, so it's not that accurate. But 27 to 25 is a much smaller fractional jump, which is why it's so close to exact.
@bobon1232 жыл бұрын
Actually, you get good results when you are just above a perfect square, but very bad if you are just below. Sqrt(24) -> 4 + 8/8 =5. A better formula, that indeed works well whenever you are close to a perfect square from both sides, is N+R/(2N+1) instead of N+R/(2N). This works because the distance between two consecutive perfect squares N^2 and (N+1)^2 is 2N+1. Taking the residual over 2N+1 would be basically looking at a weighted interpolation between the following and previous perfect square. Graphically, what this would be doing is basically approximating the parabola X^2 with a series of segments connecting all perfect squares. So the result is close to perfect if the number is close to a perfect square, and far away if it is in the middle between two perfect squares.
@luxraider53842 жыл бұрын
yeah of course because x has to be way greater than dx (you ve already seen the formula above in the comments.
@guilhermeshiba31352 жыл бұрын
@@joebangles9951 KZfaq doesn't allow links
@pentelegomenon11752 жыл бұрын
I guess the "heavy lifting" of the trick is the first step, where you figure out the rounded-down square, and if you know the rounded-down and rounded-up square then you might as well just make a rough guess.
@talancorwell2 жыл бұрын
You can actually invert this method to go off of the next perfect square, by inverting your addition/subtraction operations. i.e. √95 -> 10=√100, 100-95=5, 10-(5/20)=9.75 √95=9.747 Using the normal method gives you 9+(14/18)=9.777, which is clearly less accurate. You'll find that the method that uses the smaller numerator (aka the one that uses the closer perfect square) will be the more accurate method.
@MathyMegaMan2 жыл бұрын
One improvement: Add 1 to the doubled number in the denominator. So, instead of calculating the square root of 27 as 5 + 2/10, do it as 5 + 2/11. On average, this cuts the amount that any given solution is off from the actual amount by half.
@kid84672 жыл бұрын
genius.
@txtce2 жыл бұрын
yeh but kinda a hard fraction to work out mentally
@MathyMegaMan2 жыл бұрын
@@txtce In this case, definitely, but if we were doing, say, the square root of 94, which would be 9 + 13/18 with their method, and 9 + 13/19 with mine, I wouldn't say that 13/19 is that much harder than 13/18.
@tacobender16432 жыл бұрын
How about difference in squares? For some reason I cant wrap my head around doubling the square root, i dont understand where that part comes from. But what about this method. I just thought of this but im positive someone else has invented it.I 87 is between 81 and 100 (9 and 10 squared). The differece is 19 and you have 6 remainder. 6/19 is around .315. I know its not as accurate but it makes more sense to me. Also 650. 625=25 676=26 676-625=51 650-625=25 remainder 25/51= .49ish So 650squard root is 25.49
@MathyMegaMan2 жыл бұрын
@@tacobender1643 Yep, that is actually the basis behind what I mentioned. The 'doubling of the square root' comes from the fact that the difference between the squares will always be halfway between twice the lower square root, and twice the higher square root. So, in your first example, 2 x 9 = 18, and 2 x 10 = 20. The actual difference is 19, as you noted. So, if you add 1 to double the square root of the lower number, you get the difference between the squares.
@senkumeow5095 Жыл бұрын
Man,you're making me fall in love with math once again
@ELIZABETHOkiwelu-fh4qi9 ай бұрын
It's how he calculated The decimal aspect of the second question. Genius!
@Taervis2 жыл бұрын
The material in this video is application of the binomial approximation: sqrt(1 + x) = (1 + x)^(1 / 2) ~ 1 + x / 2. Let the value under the square root be written as a + b, where a is the closest perfect square and b is the remainder (difference from the perfect square). You then have sqrt(a + b) = sqrt(a) * sqrt(1 + b / a) ~ sqrt(a) * (1 + b / (2 * a)) = sqrt(a) + b / (2 * sqrt(a)).
@IckusVickus2 жыл бұрын
I like your funny words, magic man
@michelevalenti852 жыл бұрын
I came here looking for this, thanks a lot! I think this should have been added to the video.
@scorpionkiller192 жыл бұрын
If you say so
@guillaumestl28592 жыл бұрын
Necessary to add this in the video, in math you need to be precise, you can't just drop a few examples and assume it works.
@dilldozer76042 жыл бұрын
Well that's a whole lot less fun
@twisted55762 жыл бұрын
I love how he keeps asking how you did, it's one of the many things he does to make this video nice and engaging
@quabledistocficklepo35976 ай бұрын
THIS method I find easy and useful. Of course, I might forget every single step, but a few second's refresher will quickly "bring me up to speed."
@kurmet24Ай бұрын
Thanks mate Didn’t know I could just pause the KZfaq video or replay it if I was strugglin’ to keep up. You beauty!
@Mahesh_Shenoy8 жыл бұрын
It would be nice if you could show why this is true? Differential calculus. So we should thank Newton for this :P Say you need to calculate root(x+ dx) where dx is much smaller than x Here x is the nearest perfect square, and dx is the extra number We say let y = root(x) and y+dy = root(x+dx) Our goal is to find dy, we can differentiate y dy/dx = 1/2root(x) Or dy = dx/2root(x) Hence our final answer is root(x+dx) = root(x) + dx/2 root(x) You can now understand why he is taking that extra number, and dividing by the double of root of the nearest perfect square. This also explains, why you cannot use this method for squaring numbers, where the extra number is comparable to the nearest perfect square, the differential approximation works best when dx is much smaller than x (atleast 1 order of magnitude, else you get horrible answers :P)
@zainabgulshanara9228 жыл бұрын
Thank you for this. :) It feels good to know why certain simple methods work.
@aaronclark25998 жыл бұрын
you can also try looking up "binomial theorem" if you are not that familiar with calculus. this approximation is the first two terms in the expansion of (a^2 + b)^(1/2). you can also use (a^2 - b)^(1/2) as others have pointed out, if it gives you a smaller "b". the smaller the value of "b" gets compared to "a", the better the approximation gets. this is because it makes the terms you are ignoring in the binomial expansion after the first and second become smaller faster. this is why he says to use the perfect square closest to the number you are taking the root of.
@wduandy7 жыл бұрын
You mean the Newton-Raphson method?
@fatumasulieman26667 жыл бұрын
no science here
@fatumasulieman26667 жыл бұрын
true
@nunogue8 жыл бұрын
I got curious and tested out this aproximation method in excel against excel's internal square root number. I calculated the percentual difference between the aproximation and the actual sqrt given by excel. i worked it out from 1 up to 1600 So it happens that the diference (as expected) resets to zero whenever you get to a perfect square (like 36 or 100...), and then increases as the number climb to the next perfect square. When you plot it the graph looks like the teeth of a saw. What's cool is the fact that as the numbers go up the teeth go wider and shallower, so the aproximation get's better and better. The absolute worst case is number 3 that as a square root 1.73205 and the aproximation yelds 2, thus giving a percentual difference of 13.397%. But, for instance, 1598 has a square root 39.97499 an the aproximation yelds 39.98718. That's 0.03048% difference. (at 1600 it resets the differences as it is the square of 40)
@cnn-news.248 жыл бұрын
+Nuno Gonçalves Thanks for sharing your findings! BTW your descriptions bring so much more to this method. Thanks again.
@nunogue8 жыл бұрын
+tecmath I should be the one doing the thanking for the brain candy, so... Thank you. ...Keep them coming. BTW, if you want, i can send you the excel file. Regards
@dananajj8 жыл бұрын
Percentual is not a word. "Percent" difference.
@nunogue8 жыл бұрын
+Danana J: Thanks. It's always good to know. Allow me to excuse myself, English is not my native language and i'm not using a spelling checker. Most words that exist in my native language have an English counterpart, so i tend to apply them. Sometimes, such as this one, that is not the case and the word doesn't exist in English (rare). Needless to say we have both "Percent" and "Percentual" (the later meaning that we are talking about something with percent-like caracteristics). Regards.
@dananajj8 жыл бұрын
+Nuno Gonçalves Yes i undertood your use of "percentual". Btw this "amazing" trick done by tecmath is just a Taylor series approximation, which is most mathematicians use to do these "party" tricks.
@MaZe741 Жыл бұрын
would have been nice if you also did an example where you take the next bigger perfect square, such as the square root of 1000, where the next bigger one is 1024, the difference is 24, 24/64, and you subtract this from 32. the next lower perfect square would be 961, which is a little less known - or even harder to calculate actually.
@brucecohen30012 жыл бұрын
This is like pure mathematics. There is no practical application of this knowledge.
@sirwaffel52364 жыл бұрын
He's talking like there's someone sleeping in the next room
@johnnations59323 жыл бұрын
Or the same room:)
@billybobthornton81223 жыл бұрын
Shhhhh!
@barpsoon30313 жыл бұрын
An SJW.
@D.KlWA-aG3 жыл бұрын
The sleeping elephant holding its ears
@harryroberts3883 жыл бұрын
Cause he's an aussie
@normallymute01312 жыл бұрын
This was genuinely interesting. I wish you were my teacher, I’d listen with all ears because your teaching methods are actually enjoyable
@Clips.12810 ай бұрын
i’ve been in a cambridge math class for the past week learning this and didn’t understand this. thanks to random youtube guy i learned it in 2 minutes
@burnyizland Жыл бұрын
You do the same things I do, breaking equations down into their easiest to deal with parts, do the math on them, figure out the remainders, then put everything back together. I'm not trained in math, in fact I dropped out of 10th grade math and then had to play major catchup for my science degree - my hydrology work almost killed me! But I'm autistic and have a high I.Q. so I managed somehow. I've always done this, and done it faster than I can explain the steps, so my teachers in grade and high school hated me not doing it their slow way + showing my work was hard. I LOVE math. My son is 7 and is a lot like me. I'm starting to show him breakdown tricks already, they make math so much easier and he likes to be able to do it 'the magic way'. I can be bad at explaining more complicated examples (I can't slow my thoughts down enough to pick the steps apart some times) so I'm going to sub you and have him watch. Thank you for this resource. You are a treasure!
@togishere3 жыл бұрын
They should literally teach this in schools. I'd say 7th grade would be a good time to learn this. (Or maybe don't teach it, just so your viewers have an edge over the average person :))
@professorx30603 жыл бұрын
But this is learned at school, infinite series approximation
@eitankalfa78362 жыл бұрын
No they shouldn’t, he is doing this through a method of calculus, which is hard to understand that early
@eitankalfa78362 жыл бұрын
@Milo Dog mabye, but either way this isnt rly useful cause u usually can just use a calculator.
@carlcool202 жыл бұрын
@@eitankalfa7836 Nahh this is extremely useful for competitive exams where the calculator isn't allowed
@knightenchanter79082 жыл бұрын
@@eitankalfa7836 calculators should never be allowed in schools. It's good at making you bad at math and nothing more. Everything should be done manually. There are more ways to calculate square root manually than this. They could teach those if this is too difficult.
@CNSninja2 жыл бұрын
Dude, this is so good. Square roots have always been difficult for me. I love math and I'm not bad at it at all. It's the class I did best in all through school. Every year I'd get high 90's in math while I tested very poorly in most other subjects. I never fully memorized my multiplication tables though because my brain just works differently, probably partly because I'm dyslexic with numbers, so that made everything else a little harder, especially square numbers. I never would've thought of a trick like this but once you explained how it worked it instantly made perfect sense. I feel like this trick just gave me a better sort of understanding of, or intuitive feel for, square numbers and their roots, like over all, as a concept.
@neworder45612 жыл бұрын
What about integration and calculas? You were good at that too?
@marshenrobot76002 жыл бұрын
Didn’t know Bruce had a math KZfaq channel.
@wesleyw.terpstra1902 Жыл бұрын
What a clever regrouping of the Babylonian method / Newton's iteration! To find the zero of f(x) = x^2 - a: x - f(x)/f'(x) = x - (x^2 - a)/2x = 0.5*(x + x/a) ... which is the Babylonian method, but that also = x + (a - x^2)/2x ... this method.
@jacinths943 жыл бұрын
I see why you have a million subs. How you teach is simple, clear, and direct. Thank you so much for your lessons!
@jbriscella2 жыл бұрын
It’s nice when teachers can be teachers and not forced into some regimented way of explaining things handed down by an out of touch and overly academic administration.
@user-fb4zo8wd5n2 жыл бұрын
For those who finished calculus 2: this is the first order term of a Taylor expansion of the square root function. Nice explanation.
@johngreen35432 жыл бұрын
Or simply, the tangent line approximation
@rtrevellyan2 жыл бұрын
Exactly. This is essentially how we did distance approximations in 16-bit video games back in the 90s.
@howareyou4400 Жыл бұрын
The math behind the trick: High school physics approximation/First order Taylor series expansion. (1 + x)^n ~= 1 + nx for small x => sqrt(1+x) = (1+x)^(1/2) ~= 1+x/2 => sqrt(a^2 + b) = sqrt(a^2(1+b/a^2)) ~= a(1+b/(2a^2)) = a + b/(2a)
@aagbayani2 жыл бұрын
ive always wondered how people were able to do this in their heads without calculators and now i know how. thank you youtube for putting this in my recommended
@vizender4 жыл бұрын
Me at the begening : lol he is just gonna say « use a calculator » At the end : yep, pretty accurate
@anjaninator4 жыл бұрын
How
@bengraham94483 жыл бұрын
Beginning*
@ViewoPlays3 жыл бұрын
No it’s not.
@smalltrashman42273 жыл бұрын
What are you talking about. He didn't say anything remotely similar to that.
@enterchannelname75143 жыл бұрын
@@bengraham9448 biggenengue*
@zuklar2 жыл бұрын
And just like that... 32 years into my life hating math... I now know what a square root is and was able to pause the video and complete each of these problems. Thank you! That was surprisingly fun!
@nathanhyatt6 ай бұрын
This is a GREAT way to *approximate* (but not *calculate*) the square root. I appreciate the tip in either case!
@Atoggod2 жыл бұрын
I use 2x+1 as the denominator as a closer approximation. 2x+1 is the size of the scope between squares. Did this in HS when I forgot a calculator (1990).
@T4ckyy4 жыл бұрын
Chinese adults: *this 2nd grade in china*
@imanand1014 жыл бұрын
Indian kid: Hold my Mathmatics Notebook 😂😂
@Chill-yv4gg4 жыл бұрын
anand kashyap OMG RIGHT 😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂👳🏾
TheAnimationGalaxy it’s not VERY racist but it is a stereotype and can offend some people
@gillianross72254 жыл бұрын
Nice job conforming to be in a rasict who uses hurtful stereotypes
@fathima54222 жыл бұрын
Thanks a ton, you're a lifesaver! My statistics teacher made this way more complicated by doing it through long division and I was lost. Now I'm an ace in finding square roots!
@johnmccallister18182 жыл бұрын
Wish I had this guy for a math teacher back in school.
@SadisticCanada2 жыл бұрын
The algorithm has brought me here, and for what reason? Quick Maths