This method is really old . My primary school taught me this over sixty two years ago when I was preparing for Common Entrance Exam. Her name was Miss Valerie Retemeyer. God bless this dear lady

That was exactly the method I've been shown in school 35 years ago. I have forgotten the exact algorithm, and now that my daughter has asked me if it is possible to calculate a sqrt by hand, I am happy to share that with her. Thank you, sir!

I am approaching 80 and this is the first time someone has had the ability to explain it to me. Thank you!

I always remember this method as Horner’s method. Your description of the different stages is how I remember it, except that at each stage you double the number above the line, I.e ‘2’ becomes ‘4’ then ‘29’ becomes ‘58’ then ‘291’ becomes ‘582’ etc and then determine the red digit as you describe.

I used to teach this all the time in Ontario. Past the initial step, I used to say " Double the top, write it on the side leaving a space. Whatever fills that space must also go on top" Seems easier to do than your adding procedure for the side number.

I remember my Dad patiently, and carefully explaining this to me in Grade 3; while I sat in astonishment, shock and fascination thinking: "But I just wanted the square root of 25!" I did remember the details well enough to put it all together some years later in high school, when my math skills were somewhat more mature. Thank you for prompting a fond memory. One point my Dad made was to place each digit of the result above the corresponding group that generated it; making placement of the decimal point quite obvious. Love you Dad. Miss you every day.

Most useful - I had learned this in school about eighty years ago, and later after learning the easier method of Log table-use did not have to use it! However, delighted to be reminded of this method again that should not be forgotten and remains useful for teaching youngsters that creates their interest in learning maths comfortably. - Ashit Sarkar (89 yrs young)

The last time I saw this was when I was in high school-1956 through 1959. We did it slightly different, with the writing of the numbers to the right of the system. We also left the square root sign in place instead of drawing a division box. We did need to remember to put a +/- in front of the answer, however. Thanks for the memories.

Two details. I would describe what you do as multiplying by the last digit. I would also write the digits of the result over each GROUP. That way the decimal point automatically comes in the right place.

2 questions: 1) Who is credited with discovering this method? 2) Why does it work and where can I read about that?

I am the class of 1957 (yeah, that song) I was taught this by one Mr. Lynn Mauntner (amazed I remember his name). He also taught us logarithms, slide rule using a log log antilog slide rule (a four foot long one hanging on the wall) and after class he would show the few of us who hung around how to do things not in the syllabus for the class, like taking the cube root. I remembered (mostly) how to do the square roots and after you did the second step I was back in the rhythm (thanks) . Taking Cube roots I can sorta remember but I will need a bunch of hand holding (never used it after the precalculus course in 1956)

I'm 40, an engineer and part time math and science tutor, and since high school I've been pretty good with being to do everything mathematically by hand. And I've never learned this method lmao. Love it!

Thanks! I learned this in 5th grade (1960) from Mrs. Simms, but then forgot it. I looked around a couple of years ago and everyone on the internet wants to do a much more complicated and barely more accurate method. But this is more than adequate. Most of the time I want to use it is to estimate the Square root of a hypotenuse to the nearest unit value. Basically, "How much would we save if we cut across instead of going around?". Unlike the other methods, I can see doing this in your head.

I learned this method in elementary algebra class in junior high school. Most kids didn't have calculators back then, so the teacher taught us how to compute square roots with pencil and paper. But I totally forgot how to do it afterward. It was one of those things you learned to pass your exam and then dropped.

I learned this method in my high school algebra class, in 1979. This was the beginning of the era of hand held calculators. One day, during class, I went to my teacher’s desk and asked, “Before we had calculators, how did people figure out the square roots of numbers?” He showed me this same method. All these years later, I have never forgotten it. Thank you for sharing a video about this.

Thank you. Very well done. I am a retired QC mechanical inspector. Always did my math with pencil and paper.

At 5:12 you get the 58. A much simpler way to get this is to DOUBLE the EXISTING answer gotten SO FAR. Double 29 = 58. Do the same at 6:41, doubling existing answer (29) to get 582. At 7:08, you talk about decimal point. This is much simpler if you write the answer digit over the last pair dripped down (spacing answer digits out). This way the decimal points will be vertically aligned. At 8:24 you double 2911 to get 5822. To illustrate the alignment, I show the final result calculations aligned as I suggest. 2 9 1. 1 4 4 8 47 65.23 47 4 58 4 47 4 41 582 6 65 5 81 5822 84 23 58 21 58228 26 02 47

I am old enough to have gone through grade school pre-calculator. Never taught this, but, now, I'm going to watch this video again, and do a few square roots by hand. This is amazing. (To the nay-sayers - if you get a wrong answer, you messed up a step. As a math teacher, I'm very careful before declaring a book has a typo, or a fellow teacher, a wrong answer.)

This method of solving square roots reminds me of my childhood 70 years ago. This is what we call it mental math. I still remember this method and used it my whole life when required without a calculator or computer. thanks for refreshing my knowledge. There was no calculator those days.

OMG! I had learned this in the 7th or 8th grade and back then this was easy to me and I liked it. Then over time I forgot how to do and spent the next 10 or 15 years trying to find someone that knew how to do square root by long hand (as we called it) and never did find out how to do it again. And then you come along and retaught an old fart how to do it again. I was spell bound when you started then little by little it all came back, amazing. Thank you very much, although I don’t really use it or need it but just seeing it one more time was fun. Thank you for making, now a 73 year old man happy for a little bit. Many times over the years I would tell people that I once could do square root on any number by long hand and they either just looked at me like I had three heads or they just laughed their asses off. Ahhhhhh, now I can go in peace. 😂

This takes me back to my first year of secondary school. So aged 11. Afterwards we were taught to read off the log of a number from a book of tables and divide it by 2 and then take the antilog. This was also back in the days of slide rules. What was great about them is you had to have an idea of what the answer should be so could catch errors quickly and get the decimal point in the right place. Even at University we had a lecture on fast estimation. Look at a problem, simplify the numbers (ie. PI is 3), do a rough calculation and then find you have gustimated the solution accurate to two decimal places. Calculators are great but they have killed people when they give rubbish answers and are believed.

We did it in high school in class 8th and I can still do any number by hand. Just want to add that instead of adding 9 into 49 the simplist way is just double the 29 at the top in answer place. Which still give you same thing. Similarly in first place double the 2 in black color instead the red one. Anyway your way is also correct!!

brilliant! i remember learning a method of taking a square root from a book but never mastered that method, especially since I learned it on my own (they didn't teach taking square roots from all sorts of numbers, only the obvious ones). Thank you for making this video! Very clearly taught, too. :)

My 89 year old dad was showing my teenage daughter this the other day. He said he learned this math when he was a kid. He says they don't teach kids how to do math today...everything is done with calculators. So true.

Without paper or pencil, the sqr(6) must be between sqr(4) and sqr(9), that is, 2 and 3. Linear interpolation of 6 between 4 and 9 gives (6-4)/(9-4) = 2/5 = 0.4, which is the offset of 2. So, the result should be approximately 2+0.4 = 2.4.

Great stuff, I've been a math nerd for a long time always happy to see things like this out there for the world to learn.

My father (who finished school in 1927 at the age of 14) taught me this method when I was about 10 years old. A couple of years later in grammar school the maths teacher (Mr Hodges) was teaching us square roots by prime factor which only worked for perfect squares. He claimed the only way to calculate the square root of a number that was not a perfect square was to use log tables. When I told him I could calculate square roots without log tables he basically said I was wrong. So I went to the blackboard and showed him the method described in this video. He was amazed and, to his credit, he apologised to me. I then showed him how to calculate cube roots by a similar method.

I'm 63. When I was in 9th grade, I learned to do this in algebra class. By the time I took chemistry in 11th grade, we had calculators that would take square roots, so I never used it, and forgot it after a few years. It's amusing that it has "come back around." Nice job of teaching it. The reason you add the last digit to the number on the left is because you are doubling the number on the top (the estimated square root). This is because (x+y)^2= x^2+2xy+y^2. If you untangle that expression, you can see what's going on and why this method works. (x is your estimate, y is the additional part of the square root you are trying to find). I enjoyed your video, thanks!

lot of people are saying this is underrated but it has been used in india from a lot of time

Great explanation ! When teaching a subject that you are very familiar with, and your students are not at all ... NEVER use words like "simple" and/or "easy" in your explanation. Rather, show enough examples such that the students will make a connection and understand the concept. Not everyone will grasp it no mater how many times you show it. That is just the bell curve in action.

For whatever it's worth, I was taught this method in the sixth grade in 1960 in private school in New York City. Everyone in the class got it even the poor students.

I remember my second daughter in 6th grade doing this, and she had taken the number out to 6 digits, but got frustrated because the calculator she used to test "her" number didn't match the tables in the calculator. I used mine at the time to shew her that her number was correct; it was a cheap calculator she was using, and it didn't give all of the decimal places. No school like the "no tech" old school, i.e., Pencil (with a good eraser) and Paper! Thanks, Tet, for the excellent video!

I can’t believe that I was never taught how to do this. Thank you so much.

Thank you, man. I cannot believe that the best explanation for this is coming from such a small channel. Keep up the good work.

I learned this method in Jr. High, back in 1966 and have taught it to many GED students. I also learned to do cube roots long hand but don't recall the method. I told my GED students that this is the method that you use when you have no calculator, such as when you are on a deserted desert island where it's an important skill.

I learned this square-root process long ago when I was a kid, but I had forgotten it... just the other day I was remembering that I used to know how to do this... so I was delighted to stumble across your video today (thanks KZfaq for listing it), and be reminded of some fun times in distant long-ago mathland.

Thanks for showing this. I had learned it back in grade school, but this refresher is great. I do have a few clarifying suggestions. 1) When the tutorial says take the number (out to the left) and add it to the "first" digit of itself, it should say add it to the "last" digit of itself. 2) In the answer at the very top, the number placed there should be "centered" over the group of numbers to which it pertains. In the example, the 9 in the answer should be centered over the group of 47; and the 1 in the answer should be centered over the group of 65. 3) Keep the decimal in the answer at the top in the same exact position as the decimal place in the subject number. That is, the two decimals should be exactly one on top of the other. This keeps everything a lot clearer.

Thank you for the video. As an advanced math teacher, I have two suggestions. First, start with a much easier example like √2 or √3(numbers whose value they might already know to 3 or 4 decimal places) and then something like √50. And secondly, then show what your solution squared equals so the viewer can see how precise your method is. Don't make the viewer have to write your answer down, then find a calculator, and then come back and compare it to the original number.

I googled how to do this a few months ago. Got unsatisfying results. Simply put, there is a formula to find rafter lengths but the square root of the rise and span is required and sometimes it's hard to figure out. I don't remember my teachers in school ever explaining how to do it and I'm sure whatever they taught wasn't this... easy to learn. I've always held the belief that if you can't explain something, you don't truly understand it yourself. Your tutorial was easy to understand.

I found this method in an antique encyclopedia when I was young. Helped me fly thru square roots in high school.

I was taught this long ago in elementary school. The difference was instead of adding the last number to the previous divisor, simple double the result above the line. (Quotient) I impressed my boss by using this to calculate the length of a hip rafter when the battery of his carpenter calculator died.

So underrated!

I saw this technique one time in junior high over 40 years ago and never again until just now. Thanks for posting!

A refresher--for a step by step that I would have NEVER recalled but was SO familiar. This is a toll that Hewlett Packard/Texas Instruments obscured since I often need the square root in the years since school.

A couple of comments: another way to do the step of finding the next digit by guesswork is simply to pretend you're doing long division and cover the last digit of the "dividend" (in the last step completed, it was 260247, and simply cover the final digit with your thumb and consider how many times the full running "divisor" (in the example, 5822) goes into 26024, and to me at least, that seems to be a simpler way to do that step. Next comment: it's helpful to know that each time he's added the last obtained digit to the running "divisor", what you're actually doing is simply doubling the entire result obtained so far. In the example, when he adds 1 to 5821 to get 5822, that number is simply twice the answer so far obtained at that point (2911*2=5822). This last observation makes it more clear how and why this whole method works. Consider what you get when you square the expression a+b...you get a**2 + 2ab + b**2. (I hope everyone knows I'm using ** to mean the operation of squaring). Every time a new digit is obtained in the result, all the previous digits form the "a" value, and the newest digit obtained is the "b" value. The 2ab is the one that's harder to explain, so pretend in his example that the number having its square root taken is simply 841, which is a perfect square. You'd obtain the same results as he did up to the point where the 9 in the answer is multiplied by 49 to get 441. Now with 841 being the number having its square root taken, the number produced when the next group of 2 digits was brought down will be 441, NOT 447, and you'll be subtracting 441 from 441 to get 0, so with no remainder, the original number was a perfect square, no need for any further steps. In this simpler case a is 20, b is 9, and 2ab is 2*20*9=360, so a**2 + 2ab + b**2 is 400 (20*20) + 360 (2ab) + 81 (9*9) = 841. The hard part to explain is why I'm working with 20 and not 2, the first digit obtained. But what's happening with the numbers he produces in red includes as a hard-to-see step a multiplication of the running "divisor" by 10 before adding on the next digit obtained. I'm sorry, that may be as clear as mud. I tried to explain it better, but the fact remains that the formula (a+b)**2 = a**2+2ab+b**2 forms the foundation for this method, with "a" representing all the digits obtained so far and b representing the next new digit in the answer.

Excellent explanation. We were made to do this in year 9. Used log tables and sin and cos tables, mean difference tables and both types of root tables. No calculator until year 10 (1978). Gave a very good grounding in arithmetic!

This is really great. I am 65 and I never heard this ever. Thank you very much !!

I was shown this method in school exactly once but the teachers didn't test you on it. Later on I was shown how to interpolate, which was resonably accurate and simpler to do.

For square roots use(10x+y)

I learnt this method at the age of nine by a teacher who saw I had an interest in mathematics, I later developed a method for cubic roots but I can't remember it now, anyway getting a slide rule stopped me using "long" methods, and the calculator stopped me using log tables, usually two decimal places was acceptable as an answer...

This is another method used in the Fortran computer language. Where D = divisor, A = answer and N = number you want square root of. Step 1: N * .003 to get D. then A = N / D Step 2: (D+A)/2 to get new D. Step 3: A = N / D Step 4: repeat steps 2 and 3 until A ~= D. Usually 3 to 5 repeats.

I learned this in grammar school, and then learned to find cube roots, which is similar, only you start by sequestering groups of three rather than groups of two.

A very fine explanation. However, the first stage is not doubling the 2, it's ADDING 2. What difference does it make? Well, the progression is purely one of addition, which makes it much easier to remember, long term, Doubling AND adding during a continuous process has no logic to it.

In this particular example, a good approximate answer can be obtained in four steps: Step1: 84765 is close to 90,000 so sqrt(90,000)=300 with difference of -5235. Step2: 300 x 2 + 1 = 601 ~ 600 Step3: -5235/600 ~ -8.7 Step4: 300 - 8.7 = 291.3

I've loved math since 9th grade and even tutored it for 6.5 years as an adult and never saw this before. Thanks for teaching me something new.

My grandmother had a PhD in mathematics and taught math in the evenings. To my parent's surprise, I loved going to her school and hanging out in her class, even though I was usually an energetic little boy. It was so cool being in a big school with all the young adults. Of course, I'd sit in the back of her classroom quietly, entertaining myself with coloring or puzzle books, never making a single sound or disturbance. One night she was teaching this method and for whatever reason I looked up from my crayons and paid attention. I actually understood the process. She asked the class what the next number should be, and no one raised their hands to answer. I meekly raised my hand from the back of the room, a bit afraid to interrupt the class (which was a strict rule I never broke), and I was relieved to see that she was not upset with me, and actually smiled and asked what I wanted. I told her what I thought the answer was and she beamed with pride telling the class her 6 year old grandson was correct. I was always excellent in math, even at an early age, a skill no doubt inherited from both my parents. I remember that class, and her teaching this method (with slight variation), and the ease I picked it up, and the difficulty some of her students had with math overall. Her smile when I answered the question correctly I'll never forget. She was an incredible woman, and I miss her dearly. Thanks for bringing this cherished memory back.

My equation is as follows. I have written down straight forward ! SQRT X ~ (X-A)/(B-A) + SQRT A A: Biggest perfect square less than X B: Smallest perfect square bigger than X SQRT B = 1 + SQRT A It works better for bigger numbers ! SQRT 111 ~ (111-100)/(121-100) + SQRT 100 = 10.523 (actual is 10.535)

I use a much faster, but imprecise method in my head, just for quicky analyses, and for this I got 281 in no time. Here's how I do it. 84,000 is 2 times 42,000 or 4 x 21,000 8 x 10,500 16 x 5,250 32 x 2500 64 x 1250 128 x 625 256 x 312 At this point you go to the halfway point between the two numbers, and decrease it a little because the graph y=x^2 is curved such that the halfway point on the x axis corresponds to a point on the y axis that is less than halfway. The halfway point is 284. I guess I should have stuck with that because I neglected all the digits after the 84.

Learned this method in the 70s. When calculators first came out my parents bought one for me. Just a simple one that did simple arithmetic and it cost $125! I wasn't even allowed to use it in class because not all the students had one. I mainly wanted it to figure out ERA and batting averages.

And this is only one reason why handheld calculators are so useful. Programmable scientific calculators (handheld, battery powered) were becoming available in 1970. I bought one at Sears in Atlanta (1971) for $150, saw it at Sears in California for $99 and bought it to be returned when we returned home from our drive to Alaska.

Nicely done. I had to teach this to Grade 7 and 8 students and the hardest thing for them was keeping the position of the numbers in the quotient. The fix I had for this made the work seem more difficult than it was but only seemed as they began the way I taught them and later ditched the part which made it look messy. Usually, only the ones who had a real problem with the times' tables had any problem at all. Then again the pocket computer came out and made everything actually harder to get across. Why learn how when all you had to do was press the square root key?

This is soooooo cool! So I made at least 20 other square-roots! It’s just too much fun! What a great method! Thanks!

THANK YOU. I have been wanting to learn this forever but I never knew what to look up. We never learned this in school.

Never learned this method but did learn (and sometimes use) the divide and average method. To find sqrt(x), divide x by a rough guess at sqrt(x). Average that with the original guess. This is your new guess for the next iteration, Just two iterations gets you pretty damm close. Example sqrt(5): Guess is 2. 5/2 2.5. Average 2 and 2.5 = 2.25. This is your new guess. 2nd iteration: 5/2.25 = 2,2222. Average this with 2.25 gives 2.2361 which is pretty close to the real sqrt(5) which is 2.236068. Of course, more iterations will refine the result.

I learned this as a "Horse and Goggle" method from a H.S. math teacher who wore really wide paisley ties and was kind and funny.

In Iran, we were not allowed to use calculators, and I believe it is still the case there. You might laugh, but we had to learn squares and square roots of 1-20, sin, cos, tan and cotans of round angles etc etc by heart. We were taught how to take square roots when we were 12 or 13, and a version of this was the method they taught us. I remember I found it a bit complicated at the time, and had to revisit it for use at high school. The version we were taught was that to get the black numbers on the left, you double the numbers above the bar. Also, to get the red numbers, you bring down only one digit first and then you divide that number by the number on the left, i.e. 44/4=9; 66/58=1; 842/582=1; 26024/5822=4. Then you bring the next number down.

I was always told to check my work. So squaring 291.14 gives us 84,762.4996 which is very close to the original number. Performing more steps will obviously improve the accuracy. Great video!

At 4:00, referring to the 49 you said add 49 to the first digit of itself. For clarity, the phrase "first digit" is relative to perspective. I write left to right so the first digit (from a layman's point of view) would be the 4, not the 9. When you said 49x9 you shut my brain down.... perhaps you should say "add it to the 1's column digit. just sayin... Great video!

Cool! I learned this method (or something very similar) in 8th grade (thanks, Lynne!). In high school I came across a book that explained how it works, based on the fact that (a+b)^2 = a^2 +2ab +b^2, and it even showed a similar method for cube roots, which could probably be extended to fourth, fifth, etc. roots.

Good technique for finding standard deviations. You take 1/4 of your total bets and then take the square root of it to find the standard deviation.

I picked up this system when I was given a book by Trachtenberg,who worked this and other calculations while in a Nazi concentration camp,writing the finalised methods on scraps of horded toilet paper. His wife eventually got him to Switzerland,where he taught the system to struggling pupils.

This is an interesting explanation, but is different from the method I was taught (other than starting by grouping the number in pairs from the decimal point). We were taught to multiply the answer thus far by 20 and then add the next (estimated) digit to that to become the next divisor. So, in your example it would be 2 (first digit of answer) x 20 = 40 and then say to yourself 40 something divided into 447. That something will be 9 so divide 49 into 447, then write that product of 441 under 447 and subtract. the next dividend becomes 665. Multiply the answer thus far (29) by 20 and get 580. Say to yourself that five hundred eighty something is to be divided into 665 so it has to be 581. At its basics, this is the same as your method, but just explains it slightly differently. I always said to my students that this was a pencil - not a pen - procedure! I learned this in the USA and taught it there. Perhaps somewhat surprisingly, when I taught in the UK, none of my fellow math/s teachers had ever learned how to calculate square roots by hand. The only colleague who knew how to do it was a French teacher who was French and had been taught it as a schoolchild in France.

Heck, I was taught this exact method by Sisters Of The Incarnate Word (Nuns) in the 4th grade over 63 years ago. And I still remember it and occasionally use it to refresh my memory. When my step daughter was in the 4th or 5th grade, I asked her if she was or had been taught this method, and her answer was "the deer in the headlights look." Very disappointing. Today's education systems are abysmal. It's why I would venture that the overwhelming majority reading this don't know the differences among "there", "their" and "they're." Oh, we were also taught to (and did in fact) diagram sentences! Subject-Verb-Object. I could continue, but I would be up past midnight.

I am in my 50's and was never taught this method. It is amazing. Who invented it ? When ? Finding square roots was one of the reasons Calculators were invented.

My 5th grade teacher Mr. Biot taught this to us in 5th grade. Was really magical to me .. and still is.

4:57, you add it to the first digit, or was it the last digit? You didn't do what you said

Thank you! I was wondering if you have a visual proof that indicates why that rule works. My students would appreciate a visual proof in addition to memorizing the procedural steps.

We used to learn this method in school thirty years ago, but had forgotten it very quick thanks to pocket calculators. Now this video refreshed my memory. Thank you!

I learned this method way back in the 80s when I was in my 8th grade in Eritrea. In step 3, after you bring the pair down on right, you were supposed to leave out the last digit of 7 (44 instead of 447) and divide the number by the 'doubled' 4 (or 44/4) to get the rough factor estimate of 9 (so 49x9=441). You were supposed to do this all along every time you drop down (leave out the last digit then divide and multiply - helps you take out the guesswork). --- Another thing, instead of doubling the single digits on left, you also could simply have doubled the entire number sitting on top of the bar each time. Still, great video presentation though.

Good organization of the data! Thank you.

An interesting method. Very curious as to how/why this works. If I needed to do this by hand I think I would use Newton-Raphson method. In the second itteration I already got to 3 decimal places.

This is amazing! I'm almost 58 yo and, beleive it or not, this method used to be taught in Greek High Schools in the late 70s! Not taught any more….Thanks for reminding me!

This guy only uploaded 4 videos, and all over 5 years ago Suddenly this video just blows up. I wonder what he's thinking...

I have not needed square roots for a long time, but watching this was fascinating. 🤗

I knew such a method existed but never saw it explained, thanks for the video. Now, for a challenge, can you make a video explaing how to calculate (by hand) the base 10 Log of a number? Of the few methods I've seen (on YT) it was either: A) a contrive i.e. easy example calculate for 10 or 100 or, B) a number whose log was know is some other base, e.g Log (base 3) of 27. How would one calculate the Log of 20? I know it's between 1 and 2 but that's as far as I can get.

Thanks! i remember learning this method in 6th grade, and in the intervening 36 years i've (somehow :) completely forgotten it. Good to be reminded

From the recent comments here, clearly some quirk in youtube's algorithm is suddenly putting this old video on a tiny channel in front of people. Fascinating. I would have thought that the way to do something like this would be to work out Newton's method by hand. But probably this is totally different since it gives one digit at a time. It might be fun to work out the algebra of why it works, and i love how the "guess the number" part generally doesn't get more difficult even as the numbers get bigger.

Chad, thanks mate this helped a lot

Excellent explanation! I learned this when I was in 3rd year of junior school (in UK) so about 10 years old. We had a very progressive young teacher who also taught us logarithms and it has been a party-piece of mine ever since. I honestly have never met anyone who could do this. The only difference we were taught was to double the answer, ignoring decimal points, and bring that down as the next divisor instead of what you showed but it comes to the same thing anyway. Do you know how to calculate cube roots? I've never been able to figure that out.

It's the only method people should use . It reminds me of how people struggled to balance equations

For a fast estimate, Just know or calculate the perfect squares 1, 4, 9, 16, 25, etc., and estimate for the fill in of decimal places. Folks thought I was Einstein as I could say these right off the top of my head. Approximately 4.1 for the sq root of 17. 4 squared is 16 and because 17 is close to 16 (1) the decimal part is numerically small also. Then would proof it on paper. Its actually 4.12 at 2 places. This is a great presentation.

This was a great explanation. I definitely needed that info like how to do the groupings, if there is an odd # of digits, and where that decimal goes. It's definitely a tricky little bit of calculation and would take me a lot longer than just plugging it into a calc... but with a bit of practice I feel like I could crank out the figures by hand if I needed to... like if I was helping check my kid's math

"easy and fast"

I'm 65 and was never taught this. Slide rule was the first tool we were taught to find square roots.

I believe this is how I was taught how to get a square root back in high school; in the early 1970s. I had forgotten it since after that I used a calculator!

He’s a fraud

Two years ago I taught algebra using Ray's Arithmetic series (published in the mid-1800s) -- this is the method used in Ray's and, presumably, all other math books of the era.

This brings back memories of when my 9th grade math teacher taught us this in 1971.

Imagine taking this apart and proving 'why' it works. It reminds me of some of the derivative 'short-cuts' we learned in calculus. We could use them but only after we learned to prove them.

This is truly radical thinking.