Japanese | A Nice Radical Math Simplification

Japanese | A Nice Radical Math Simplification | Math Olympiad

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3 ай бұрын

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@richardatkinson4710 2 ай бұрын

That algebraic method isn’t a method at all. You can’t set off on a series of substitutions in the hope that you might end up with an easily recognizable perfect square. The “problem” has been constructed from the “solution”.

@YAWTon 2 ай бұрын

I disagree. Once that it is recognized that 64^2+49^2+15^4 has the form x^4+y^4+(x+y)^4 the result follows from straightforward algebraic transformations. No guessing involved. Of course, in the absence of this insight, it is also not difficult to use basic arithmetic to obtain the result 169.

@richardatkinson4710 2 ай бұрын

@@YAWTon You are right, but my point is that the “method” outlined does not mention that insight. The double substitution is totally unnecessary. (Do you agree?) You either notice that you can factorise, in which case you should (and you did - as did I when I saw this) or you go through the arithmetic.

@richardatkinson4710 2 ай бұрын

@@YAWTon It’s over 50 years since I did any maths, but the substitutions vaguely recalled the solution to the general quartic. Is that how the “problem” was conceived, do you think?

@YAWTon 2 ай бұрын

@@richardatkinson4710 I agree that his presentation was bad for the reasons that tou mentioned. Too many intermediary steps. Apparently the problem suggests a "solution" that is invalid, but leads to the correct value (based on the assumption that the squareroot of a sum equals the sum of the squareroots of the terms of the sum).

@LuluLaSaumure 2 ай бұрын

It is a math olympiad problem ! Of course, the problem has been built from the solution : it is meant to be solved this way. This is how the math olympiad jury makes to find the best students : by their abylity to find the right substitution at the right moment of the calculus and their ability to lead such a huge calculus until its end ! In real life maths, you hardly find such calculus but in a maths competition it's classic that people have to use such tricks

@Baltie3 2 ай бұрын

I guess calculating it directly would take less time.

@oboumami6186 2 ай бұрын

You are absolutely right, it is around eight times faster.

@eduardofs6620 Ай бұрын

Agree. It seems that many people doesn't knows the basics, or how make some basic arithmetic operations (using elementary knowledge, and a pencil and a sheet of paper if necessary)

@Baltie3 Ай бұрын

@@eduardofs6620 and inclusive philosophy requires everyone to prove slowly, in small steps, that 1+1=2 😀

@rexwu504 2 ай бұрын

This is Candido's identity in disguise, [x^2 + y^2 + (x+y)^2]^2 = 2[x^4 + y^4 + (x+y)^4]. Candido used the Fibonacci numbers in his original publication.

@runninggreenhorn9185 2 ай бұрын

Haven't been doing this for more than thirty years ... and never missed it. 🙂

@joansola02 3 ай бұрын

The fourth root would have allowed for an extra simplification, giving 13 as the final result 😊

@udayabose2357 2 ай бұрын

Why not just long multiply, add, divide by 2 and then find the square root? Much simpler.

@vpgmiramar 2 ай бұрын

Nice. Elegant.

@villiamo3861 3 ай бұрын

Excellent. Thank you.

@schlingel0017 3 ай бұрын

There is no need to open the paranthesis of 4th power. You could do the second substition before that.

@ashokpandey5828 2 ай бұрын

Nice

@learncommunolizer 2 ай бұрын

Thank you very much!

@artyonehundred 3 ай бұрын

169 is 13^2, so is there further simplification to be done at the 8^2 + 7^2 + 8 x 7 stage?

@kevinsnell1622 2 ай бұрын

I think the power of math practice is working these out long hand, verbally calling out as you go, with pencil on paper. You develop so many other skills through this process. Agreed time consuming but worth the time especially if you are a slower learner.

@user-fb1qo8go1b 3 ай бұрын

Прекрасная задача и великолепное объяснение ее решения. Мне 72 года и моя профессия не связана с математикой, но мне все понятно и интересно. СПАСИБО

@indigopeach 3 ай бұрын

Ow! My brain!

@glotelu 2 ай бұрын

Siento que la pudo resolver fácilmente desde un inicio sin tanto rollo.

@lukaszek777 22 күн бұрын

Don't need to make any x or ys, after the first = you have (8+7)^4, that is 8^4+7^4+2x56^4. So now you easily divide all by 2, end up with 8^4+7^4+56^2 all under square root, do the root, done

@pingupenguin2474 Ай бұрын

I could do this, if necessary, as I was taught long multiplication in primary school !

@bladimirjgt 2 ай бұрын

Vamos a resolver el problema paso a paso.Primero, definimos la operación:[ \sqrt{\frac{64^2 + 49^2 + 15^4}{2}} ]Calculamos cada potencia:[ 64^2 = 64 \times 64 = 4096 ][ 49^2 = 49 \times 49 = 2401 ][ 15^4 = 15 \times 15 \times 15 \times 15 = (15^2)^2 = 225^2 = 50625 ]Sumamos los resultados obtenidos:[ 4096 + 2401 + 50625 = 57122 ]Dividimos la suma por 2:[ \frac{57122}{2} = 28561 ]Calculamos la raíz cuadrada del resultado:[ \sqrt{28561} = 169 ]Entonces, la respuesta es:[ \boxed{169} ]

@Blisssource 2 ай бұрын

Is this a solution or substantiation?

@terencetwentyman-jones8861 2 ай бұрын

That would give me writers cramp.....and why would I ever need to do it....

@irinabaigozina8551 3 ай бұрын

Супер мега задача! Thank you so much for it! It's perfectly cool

@learncommunolizer 3 ай бұрын

Thank you very much!

@unbeaunom 3 ай бұрын

Cool. I loved it.

@sthi3396 2 ай бұрын

A nice radical math complication.

@teej143 2 ай бұрын

The solution made the problem seem more complicated. I don’t need a calculator nor do I need to use this method to find the same exact answer.

@glennmann634 3 ай бұрын

Brilliant!

@FedorLyudogovskiy 2 ай бұрын

169 = 13^2 = 8^3 - 7^3

@Racvadd Ай бұрын

I'm pretty bad with math and i can't do all this process. If the goal is solving this operation without using calculator, based on my math memories, wouldn't it be easier just rewrite as: 64+49+15^2/2?

@yasnac7576 2 ай бұрын

Step seven you forgot the clouser ')' but it doesn't affect the final answer.thanks for the solution....😊

@saadalikhan9210 2 ай бұрын

Should've used a^2 + b^2 + c^2 form

@PatrickCazaux 3 ай бұрын

Was the first substitution necessary ?

@bvenable78 3 ай бұрын

No substitutions are _necessary_; they just make the algebra easier. I like that he did the two substitutions; it breaks the problem down into smaller steps, making it more accessible to viewers - especially those that aren't practiced enough at algebra to follow skipped steps.

@okiedoak201 27 күн бұрын

So...all this is nice and dandy...show this example by going to the grocery store and getting dinnner....

@cyprianalford3619 2 ай бұрын

OMG

@paperthinpizza Ай бұрын

169. Took me 20 seconds on my calculator. Simple arithmetic following the order of operations. No need for fancy math on this one

@tiramisu00 2 ай бұрын

±169

@MathSync 3 ай бұрын

i ❤ Mathematics

@michelvondenhoff9673 21 күн бұрын

Depends on where you live.

@gaskellr44 2 ай бұрын

Good old Pascal

@anatolykatyshev9388 3 ай бұрын

I have much better solution. Everybody knows that 64^2=4096. 49^2=2401 15^4=225^2=50625 Half sum of it is 28561, which is square of 169, also known fact.

@Swannerator 3 ай бұрын

"Everybody knows that..." - tell us that you cheated and used a calculator without telling us that you cheated and used a calculator. 🤡

@anatolykatyshev9388 3 ай бұрын

@@Swannerator Author also used calculator to find square roots of 64 and 49. It is not easier , than 64^2 and 49^2!

@olegkobyzev1884 3 ай бұрын

⁠⁠@@Swannerator no need in calculator, that numbers are small (easy to multiply in mind), and even if you not remember 169^2 you can just calculate it on paper.. every one knows

@maas_ter 3 ай бұрын

@@anatolykatyshev9388everyone knows sqrt of 64 and 49 💀

@gagwong8964 2 ай бұрын

Concur, way much better than fiddling all that ↑↓←→abxy口O∆ around 🤦🏻‍♂️

@evilnewbie11 29 күн бұрын

Now I know why we invented the calculator…

@oliverdauphin236 2 ай бұрын

Très astucieux. Bravo !

@learncommunolizer 2 ай бұрын

Thank you very much!

@JoseManuelSosaGarcia 3 ай бұрын

169

@himadrikhanra7463 3 ай бұрын

15× rootover 226..?

@user-pi2my7vk5j 2 ай бұрын

Математика как Поэзия! Им ночью снятся Арктики и Звездные Галактики, ведь математик- это Фантазёр!

@dhanasekaransundaram4141 3 ай бұрын

Very nice

@learncommunolizer 3 ай бұрын

So nice, Thank you very much!!!

@tlgergun7470 Ай бұрын

15×15

@gaskellr44 2 ай бұрын

Ans = 169 or even 13^2

@asyaasya2144 2 ай бұрын

Математика это жизнь!!!

@aadil_1998 Ай бұрын

Square root can be written as into the power (1/2).... = [((64^2)+(49^2)+(15^4))^1/2]÷2 Multiply the power with every number inside... = [(64^2)^1/2 + (49^2)^1/2 + (15^4)^1/2]÷2 = (64+49+15^2)÷2 = (64+49+225)÷2 = 338/2 = 169 Done

@MT_Hearts 4 күн бұрын

You forgot about √2 as the denominator.

@VincentLauria6 2 ай бұрын

Surprised he didn’t end it with 169 = 13^2

@richardatkinson4710 2 ай бұрын

Or start with root root…

@tamarshahverdyan2723 2 ай бұрын

140

@cantemirash 2 ай бұрын

Nice writing skills.😂

@AlenaSlavic 3 ай бұрын

Легче все перемножить , будет корень из 28561=169.

@handchess 2 ай бұрын

13²

@dwshow15 Ай бұрын

√64^2+49^2+15^4/2 ok Then, you can kick to root 😁, then outstanding is 64+49+15^2/2, 64+49+225/2, 338/2 = 169 ✔️ simple 😂😂😂😂😂

@stuartcockroft4365 2 ай бұрын

328

@Shirokuma15 3 ай бұрын

No, this is too long..sometimes question like this in a test only give you 1 to 2 minutes to solve,.

@fernandopobletebyfepo4820 3 ай бұрын

Prefiero seguir programando en asembler

@babsiw7164 2 ай бұрын

Wer brauch sowas

@vicenteayllonperez2879 3 ай бұрын

Y no le veo ningún aporte a las matemáticas

@guptajii7495 3 ай бұрын

120√2 solution 😢

@gagwong8964 2 ай бұрын

Are we not doing √ as the last step to get ±169 as answer?🤔

@mickaelbazola849 2 ай бұрын

No, a square of number is positive

@go_gazelle 2 ай бұрын

In algebra, the radical sign typically indicates the positive root only. A ± sign in front would indicate both roots. (y = sqrt(x) has no negative values for y.) However, I wouldn't say it's wrong if you include -169 as a second answer. I actually like that since the problem presents as arithmetic.

@gagwong8964 2 ай бұрын

Thank you both for clearing my doubt.🙏🏻 I indeed went back to read about the basics . It says something like this : square root of a number is always positive, only in functions or equations like y=x², x has two values, the positive and the negative.

@go_gazelle 2 ай бұрын

@@gagwong8964 I think that's basically correct. But y = x² seems like a strange example. A better example would be 9 = x². Here x = ±3. Or a = x². Here x = ±sqrt(a). Whereas, y=x² should be interpreted as a function in which there are infinite values for x.

@richardatkinson4710 2 ай бұрын

@@go_gazelle Quadratic equations have two roots.

@user-lw1ct2zc9f Ай бұрын

169. 5 minutes in mind.

@matsonnerby 2 ай бұрын

So much simpler than using a calculator 😂

@sirajuddinshaikh1883 23 күн бұрын

I know

@golavl Ай бұрын

Икату жжот. Зачот )

@phil4499 Ай бұрын

Lost me at 2.40 😮

@richardshaw6664 2 ай бұрын

Moral: when learning math, don't use KZfaq. 😂

@eduardofs6620 Ай бұрын

Can we complicate things? Let's do it! Or... how to make things worse than they really are...

@Physics4every1 2 ай бұрын

SO SIMPLE. DO THIS AND DO IT IN YOUR HEAD. If you know the rules. Solved it my head in seconds. Here's how. The square root is basically x^1/2 so using distribution that kills 2 from each exponent leaving [(64+49+225)/2] = (338/2)= 162. Easy

@LarghettoCantabile 2 ай бұрын

An interesting coincidence insofar as generally the square root does not distribute over terms. The numbers were probably chosen precisely because this coincidence is a trap.

@ArturJarosik 2 ай бұрын

I've done it exactly the same.

@philmach6585 7 күн бұрын

338÷2 are 169 btw

@russomarioaa 3 ай бұрын

Giochi di teoria , con calcolatrice vai subito alla soluzione😊 comunque ottima conoscenza👍

@hongthanhtran9944 3 ай бұрын

Thanks! Step 6 you lose )

@sharjeelshafqat6528 29 күн бұрын

Difficult and lengthy

@juliushafsteinsson7675 14 күн бұрын

Fram ÍA

@kentbrooks3227 3 ай бұрын

This is why I changed my major to music!

@loganshaw4527 2 ай бұрын

College mathematics is just different. I loved exponentials as a kid did not learn of the different elevations until later. I know equal and above but not not learn much of below. But only learned to the end of highschool.

@Lemda_gtr Ай бұрын

Calculator answer is 57.97 🧐

@ilevitatecs2 Ай бұрын

Good lord this is not even close to being an efficient solution.

@user-sr6uy2oy4x Ай бұрын

WHY NOT ASK CHATGPT TO USE DIRECT COMPUTATION AND ALGEBRAIC METHOD. NONE AS DIFFICULT AS ABOVE METHOD.

@dannyroosenboom3640 3 ай бұрын

sqr30705

@dwshow15 Ай бұрын

169 can come in just 10-15sec. 😂😂😂😂😂😂😂😂

@Kooliat 3 ай бұрын

Haaaaa bic mac

@ShoaibKhanZ 2 ай бұрын

The only mistake was canceling the root with the square. Should have been written with +/- (a+b).

@davegilmour1895 Ай бұрын

Use a calculator/phone

@sylvesterogbolu-otutu1498 Ай бұрын

If you took the square root and simplified the values under the radical sign, you will get: (sqrt(64)^2) = 64 (sqrt(49)^2) = 49 (sqrt(15)^4) = 15^2 = 225 64 + 49 + 225 338 ---------------------- = ------- = 169 2 2 The answer is 169

@dwshow15 Ай бұрын

😂😂😂😂😂😂

@UniqueNewYork27 3 ай бұрын

Guys, I just took the sqrt and squared exponents and cancel them out, then it'll be 64+49+(15)^2/2 Secondly, 64+49+225/2 Lastly, 338/2 Now you have your answer of 169, i didn't even learn this at school yet💀

@phoebe543 3 ай бұрын

The denominator wasn’t squared

@Swannerator 3 ай бұрын

I hope you pay attention in Maths class when your class gets up to this. 🤦🏻‍♂️

@UniqueNewYork27 3 ай бұрын

I didn't even learn this at school yet lol

@popolaminc6188 3 ай бұрын

🤦‍♂️Unexplainble, but you got the right answer

@irenebeltranruiz3431 2 ай бұрын

I did the same!

@CyBeatsSs 3 ай бұрын

Too much steps

@bvenable78 3 ай бұрын

I expect he did that for instructional purposes, and to make the solution accessible to viewers with less practice in algebra.

@Crusader-George 2 ай бұрын

not really, it's doable compared to sqrt thousands lol

@irenebeltranruiz3431 3 ай бұрын

Another solution First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169 Can you do without pencil and paper?

@rcyu 2 ай бұрын

Don't you have to distribute the square root to 2 as well?

@gagwong8964 2 ай бұрын

√(a²+b²+c²) ≠ a+b+c

@marcherrmann9635 2 ай бұрын

Pure coincidence?

@keescanalfp5143 2 ай бұрын

@@gagwong8964, in spite of all we see that it still works, at least for her.

@mikemercury3656 Ай бұрын

Can you go a little slower!

@GEILTOY Ай бұрын

You did too complicated. There is easy way without Calculator

@feroxnando 2 ай бұрын

Too much paper its not simplifing

@gandhimahatma3304 3 ай бұрын

I’m not advanced by any means but so many unnecessary steps. Neat little arithmetic problem though

@user-hq3uj4hx1w 2 ай бұрын

just calculated in my head and got the result of 169 without draw more than a full papersheet the root of 64 and 49 squared is just 64 and 49 plus 15 squared ist 225 338 half is 169 it was less than 1 minute

@Physics4every1 2 ай бұрын

Same here wrote my comment then came to see how other people are screwing this up.

@comdo777 3 ай бұрын

asnwer=9 os isit

@gato_catindig 2 ай бұрын

i just removed the squares and made 15^2/2 i got the same answer lol

@grafeebabee 2 ай бұрын

why not first get rid of the square root bracket by reducing the numbers to 64 +49+15^2...add those then divide by 2 and you still get 169 and the square root of that is 13....

@alexgrebenschikov4638 3 ай бұрын

Toooooo long solution

@SaiteZwei 2 ай бұрын

I'm sorry, but this is absolutely dubious click bait bullshit. The video has nothing to do with a serious mathematical solution algorithm. the solution only works for exactly these numbers. The task was developed backwards from the solution and is in no way transferable to another example.

@andyohil7465 2 ай бұрын

Are you crazy? The solution is quite simple and take never a minute to solve: (64 + 49 + 225) / 2 = 169

@MT_Hearts 4 күн бұрын

Denominator will be √2. Cannot ignore that.

@RobbieIsbell 3 ай бұрын

WFT? I DID IT IN 3 STEPS. 169

@marcherrmann9635 2 ай бұрын

Elaborate further, please....

@RobbieIsbell 2 ай бұрын

@@marcherrmann9635 Seriously? It's easy: First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169

@TonyQl 2 ай бұрын

@@RobbieIsbell you can’t do that because root of a + b is not equal to root a + root b

@brunobastos5533 2 ай бұрын

I never understand why they add so many steps . Like all numbers are 2 or power of 2. They do it like pc's not stray from the way they learned it even if the solution is infront of them