How To Calculate Square Roots - Numerals That Changed Math Forever

There's an incredible method to extract the square root of a perfect square in your head.
MIT Entrace Exam Arithmetic 1876 WayBackMachine:
web.archive.org/web/201904040...
Square root method Burning Math
burningmath.blogspot.com/2013/...
Square root method proof Math StackExchange
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Square root method Grey Matters
gmmentalgym.blogspot.com/2010/...
Hindu-Arabic numeral system
en.wikipedia.org/wiki/Hindu%E...
Laplace quote
en.wikipedia.org/wiki/History...
Laplace picture
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Abacus picture
en.wikipedia.org/wiki/Abacus#...
A similar method to extract the cube root of number in your head explained in this video:
• How to calculate cube ...
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[@TopWorldTalentHD]

Thanks Again!

[@MindYourDecisions]

Thank you!

[@TopWorldTalentHD]

@@golden_rod 🤣🤣🤣🤣

[@GOJOAMVEDIT]

​@@golden_rod😂😂

[@dollyrupadevich4145]

Thank you

[@qxattwo]

@@dollyrupadevich4145 why u saying thank you lmfao

[@xiaoshen194]

It's crazy how U still remember that algorithm from 1876!! Good memory 👍👍

[@yashasgupta8508]

@@sahilverma136 lol true

[@freddier47]

@@sahilverma136 you've missed the joke

[@xiaoshen194]

@@sahilverma136 tujhe joke nhi chamka bro😕😐

[@sahilverma136]

@@xiaoshen194 what kind of joke?

[@applmango]

@@sahilverma136 How would Presh *remember* an algoritm from 1876 when he wasn't alive? You completely missed the joke...

[@laurendoe168]

As you mentioned... this works only on perfect squares. These get less and less frequent as the numbers get larger. Perfect squares are 10% of all integers between 0 and 99, but only 5% of all integers between 100 and 199, and only 3% between 200 and 299... and this percentage gets worse and worse. Clever technique, but its use is severely limited.

[@tonybarfridge4369]

With a different method u can find the square root of any number, and at the same time discover if it is a whole square

[@lukas-po8yn]

True, but this is very useful for tests, since if you get a question asking for the square root of a number, chances are it’ll be a perfect square if it’s a non-calculator test. Not the most practical overall, but I don’t think that’s the point of the algorithm.

[@tonybarfridge4369]

@@lukas-po8yn of course 😄

[@ikigu]

@Lauren Doe Do you have a better technique?

[@laurendoe168]

@@ikigu yes.... a calculator. They really are ubiquitous now.

[@ayanoaman3179]

this is incredible!! I've always asked my teachers if there was a way to calculate roots by hand but they always just told me about using trial-and-error division. I love mental math and I love knowing the problems inside out

[@iqramohamed.]

Completely agree

[@tonyknight9912]

You can always use logs.

[@kayleechristensen8575]

How?

[@skmd.imrulhaquesakkhor4814]

Same

[@VishnuSrigiriraju]

There’s a method called long division, but that’s really confusing

[@squirlz333]

Another tip here to figure out the two options for squares that you have on the right is that the two numbers must add up to 10, 1&9, 2&8, 3&7 4&6, 5&5. So you only really need to remember 2 ends in 4, 3 ends in 9 and 4 ends in 6. 0, 1 and 5 all end in themselves. Cube also has a similarity where the last number on the opposite end of the 5 adds up to it's compliment i.e 2 ends in 8 which means 8 ends in 2 because 8+2 equals 10. Same with 4 ends in 4 so 6 must end in 6. So once again you only need to know 2 ends in 8, 3 ends in 7 and 4 ends in 4 with it's compliment on the other side.

[@sarimshabbir9742]

thanks man

[@wafiqahmed9394]

Thanks bro you just saved me from confusion

[@kerynwoolmer7288]

What if you have a number that ends in 2,3,7 or 8?

[@DropletsOfYakobii]

damn, thanks.

[@GrimacesGameNuggets]

The intended method for the exam question would be to express the number 11.56 as a fraction (1156/100 -> 289/25) then take the square root of the numerator and denominator (17/5). Solving that fraction gives the answer of 3.4, just like how the first part of the question is calculated. The perfect square method shown here is too specific to be useful in practice.

[@sharpnova2]

you are correct. but this channel never admits when it does things wrong or poorly.

[@DunderKlomp]

Of course that was the intended method, but the intended purpose of this video is to show you how problems used to be done prior to the invention of calculators. Case in point, many people don’t know that 289 is the square of 17. This approach is great to develop a ‘feel’ for squares and cubes, and to quickly ‘guess’ the answer. (289 ends in 9, so the root has to end in 7 or 3, so it’s 13 or 17)

[@tonybarfridge4369]

The square root can be found in the same way as with a whole number; just include the decimal point. Calculating 34 as the square root of 1156, then the root of 11.56 is 3.4; in reverse 1.5^2 is 15^2=225, so 2.25 is the answer, or 1.3^2= 1.69, 1.4^2=1.96, 2.2^2=4.84, 3.5^2=12.25 If u don't know the squares tables u can use IE 32^2= 30^2=900, +3x2x2x10+2^2 [124]= 1024 or 30^2 + 2x(30+32) or 3^2/3x2x2/2^2= 9/12/4=10/2/4. When squaring decimals double the decimal digits, and halve for roots

[@GlorifiedTruth]

@@DunderKlomp Thank you! This is so obvious that it saddens me it needs to be stated. The fact the original comment got so many upvotes just shows how susceptible KZbinrs are for any comment stated authoritatively. (I'm not bashing the original commenter here, whose basic point is correct. It's just not particularly relevant.)

[@biffbidderman8164]

@@DunderKlomp Meanwhile here in India we still don't use calculators

[@realitydisillusioned1544]

The square root of 11.56 is actually a lot easier to calculate. 11.56=1156/100=289/25 The square root of the denominator is apparently 5, whereas the square root of the numerator is 17. Therefore, the square root of 11.56 is 17/5, which is 3.4.

[@amtj8573]

kinda cool

[@manog8713]

or even easier in this case anyway: the square root must be less than 4 and greater than3. Since we know there is an exact answer, the nswer can only be 3.6 or 3.4; we then try each of these and seet 3.4 is the correct one. The best method is one to work for a whole range of numbers where the earier methods may not work.

[@annathegirlboss4886]

That’s what I was thinking too

[@swng314]

it feels "lucky" that it just so happens that the fraction reduced to lowest terms just so happens to have perfect square numerator and denominator

[@realitydisillusioned1544]

@@swng314 I think it is because the number is aimed to be a perfect square so that the number could be somehow reduced. If the number is a perfect square in the beginning, turning it into a fraction apparently yields a perfect square denominator, which is 100, and thus a resulting perfect square numerator. In other words, if the number is a perfect square number with even digits after the decimal point, it should be well reduced using this method (turning it into a fraction).

[@iikpsyt4619]

You just saved me from my destined doom of failing tomorrow’s math test. Thank you! I appreciate the hard work you put into your videos.

[@MCHamii]

so? what do you think?

[@thomgizziz]

no because it can only calculate roots where the answer is a whole number... it comes out with wrong numbers if the answer has decimals.

[@felipeaugusto2600]

News on the test???

[@sandergustavmichel1217]

So what happend?

[@innocentsupra]

I guess we'll never know...

[@sorsocksfake]

Nice! I had most of it (calculate the first digit's range, then pick the second digit's options) but beyond that I just had to try it. Which in fairness is quite doable with two-digit numbers, and 80% of the time it's an easy guess which it'll be anyway. 4 and 6 aren't always intuitive though. The x5 trick does make this faster and more secure

[@TolaseRichard]

b

[@olegmoki]

b

[@eowmob]

About 40 years ago, when I was in school, our math teacher got mad we weren't able to see simple squares like 169=13^2 . So she ordered us (and checked each one of us individ.) to learn 1..25^2 by heart. I hated memorizing tables or dates, but I had one of those 38-sth program steps programmable calculators (in 2 programs, could only loop to the start of it, only one cond. jump, max. 7 variables etc..). I managed to code a small program asking random perfect squares in a given range, counting how many sqrt you guessed right and how many you were asked for. After a short time 1..25 was no challenge anymore, so I went to 1..100. It caused a mass hysteria in our class: Many kids asked me for the code, bought a compat. calculator (there were 1 or 2 cheaper models that could still run the same code (but lacked some statistics functions)), some even asked me to enter the code for them. In every break pupils sat there solving 1..100^2 squares challenging each other for sqrt/time (you had to stop the time on a sep watch, the calc couldn't do it.). Since then I'll never forget any of the smaller squares, and yes, we developed a similar sense for sqrt at that time, even though not that formalized. And, on that calc, I really learned efficient coding with what you had. Thank you for bringing up this pleasant memory of my past.

[@Elliamy01]

That sounds insanely cool. Props for making that back then!

[@anandk9220]

@@Elliamy01 Just for info that I'm an Indian, IB/IGCSE And Indian Curriculum Math Teacher by profession. I don't know what this person has said in the video. Here's the best trick : TO FIND PERFECT SQUARE, CUBE OR Nth POWER OF ANY NUMBER : Just split the number into TWO parts in terms of place value, assume first part as A & second as B, and then use (A + B)^2 expansion. Example - 83 = 80 + 3 A = 80, B = 3 So, 83^2 = (80 + 3)^2 = 80^2 + 2 × 80 × 3 + 3^2 = 6400 + 480 + 9 = 6889 Similarly, 137^2 = (130 + 7)^2 = 130^2 + 2 × 130 × 7 + 7^2 = 16900 + 1820 + 49 = 18769 Similarly it's possible to calculate cubes and higher powers of ANY number using the binomial expansion (using Pascal triangle coefficients). TO FIND SQUARE ROOT/ CUBE ROOT OF ANY PERFECT SQUARE/ CUBE : By the way, all those who don't know this, there is an amazing 2 to 5 second technique to find square root of any perfect square, preferably a smaller number. Note that every group of two digits from right (starting from unit's place) to left will contribute to ONE digit in the square root (You can append 0 to highest place value as and when needed to complete two-digit group). Example - Square Root of 57121 1. Focus on unit's place and analyze the unit's place of square root (either 1 or 9, as both 1×1 and 9×9 ends with 1) 2. Temporarily leave the LAST TWO digits and focus on the remaining part of number. (In this case 571) Now locate this remaining number between two perfect squares. (In this case, 571 lies between 529 = 23 squared and 576 = 24 squared) 3. Since 571 is closest to 576, the square root must be closer to 240. Hence, Square Root of 57121 = 239 All dear friends, in case you are or want to be better at calculations, I'd like to share an app with you. Do try the 'Math Tricks' app by Antoni Ion from Google Play Store. Extremely good brains can try 'To The Bitter End' mode wherein they even ask 1885 squared and stuff at higher levels. [ Note : I tried 'To The Bitter End' mode many times and after reaching 163 to 165 levels, I accidentally pressed back button mostly everytime to wash away my hardwork. Finally with tons of patience, I strongly fought for 4 straight hours or more and completed 204 levels and then happily declared my calculation innings and stopped there ! ] 😂😄 You may also try Hard Math Game by marcin.magician from Google Play Store and reply your experience. In case you're interested in solving Math puzzles, do visit contestcen.com and go to Site Map (with various puzzle pages like Digits, Easy Math, Tough, Harder, Geometry, Convergence, Primes, Squares and Powers etc.) Highly skilled and interested minds, do visit contestcen.com/geom.htm and try the following questions - 1. Circles in a Square 2. 4 Tangents 3. 5 Spheres 4. TetraSpheres Thank you. Love you all. 😙😙😙

[@Oscar-vs5yw]

Wow that sounds cool! I did the same thing except on a school Chromebook (was only 10 lines in python), much easier than what you did back then

[@Alalpog]

You sir are amazing!

[@eowmob]

@all. Ah, I'm flattered, that's just too much honour. It was just something a curious teen fascinated by math and the idea of coding did. But surely the math teacher and calculator inspired me and formed my later life. Years later I got a phd in maths at computer algebra / representation theory, did some years of math research, now work in IT-security (research jobs are badly funded and create a bunch of personal/family restraints)

[@bigJovialJon]

It seems to me it's easier to start on the left (hundred's and thousand's places). 1156 is between 900 and 1600, so the answer is between 30 and 40. It's closer to 30 since 1156 is below 1225 (35 squared). The one's digit of 1156 is 6, so try 4 as the one's digit of the root. 34 * 34 = 900 + 2*120 + 16 = 1156. That method also helps you narrow down square roots of numbers that aren't perfect squares.

[@siliconvalley577]

@@JustAnotherCommenter 69=35+34, is the difference between 35^2 and 34^2, same for any consecutive squares

[@joao-im5en]

@@tonybarfridge4369 Do u know any QUICK method to know if a number is a perfect square? I just know verify it by prime factorization.

[@tonybarfridge4369]

@@joao-im5en The square below and above the number can be quickly narrowed down, from which it becomes clear. To be more precise IE SR 46 is closest to 7 and becomes 7- 3/(7x2)= 3/14= .21, 7- .21= 6.79

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@herbertlong3981]

You know it is very easy to learn a simple method to evolve the sqrt of ANY number at all, perfect square or not. It wont matter. All you are doing is trying to find square roots by multiplying numbers together until you happen upon the sqrt, This is a rather hilariously naive way to find square roots For 1156. Start at the dec point and divide in groups of 2: 11 56. Put a line over the top -- this is a long division process, so make it look like one. What is the sqrt of 11? It is 3. Put it above the line in your LD configuration, this is the first digit of your root. Square the 3 and put the 9 under the 11and subtract . You get 2 Bring down the next group of 2, which is 56. So your new remainder is 256. In a workspace beside the LD configuration, multiply (3) your current root by 20 = 60. This is your new divisor. 60 goes into 256 4 times. Add 4 to the 60, multiply by the 4 = 256. Put under the 256, subtract. you get 0. You are done because this is a perfect square You could have been trying to find the root of, say, 1186. You can use the above process to find the answer to any amount of digits you require, and quite quickly. Just did it, I got the answer to 5 digits in less than 2 minutes. You wont, with your method, find the answer to 5 digits in ANY amount of time, because your method cant do that Just learn a method to find sqrt of ANY number. Period. It is very fast, simple and it will take about 1 minute to learn the process, and it is so simple you will remember it forever. Being able to find the sqrt of only perfect squares is a perfectly useless talent You can also teach yourself the find cube roots this way.

[@scarlett_brown]

who else is here cos of university war? 🤣

[@vhrxxooo]

😂

[@meenuvish7388]

Me 😅

[@nninheaven7112]

😢me

[@thecheesefactory32]

me💀😂

[@Dedlol323]

Me…😅

[@TE5LA-GAMING]

4:50 You can also just take the 2 and multiply it by the next higher number 3: 2x3=6 and compare the remaining 8 in 841 to 6. If it's higher, you use the higher number (9). If it's lower, use the lower number (1). 8 is greater than 6, so the number is 9.

[@PixelionRules]

This is known as Estimation Method, still taught in my school- We take the numbers in pairs and find the closest root, combine them and form an estimated root.

[@PixelionRules]

@Dark nope, you do it from the left in that case For example if there's just one number over there, you find out if it's greater than 1² or 2² or 3², you have put the number smaller than the number. For example, if there's a number 1089, The first two numbers can be paired. 3² is smaller than 10, so we put 3 aside and cut off 10. Now 89 is left. We add the first number we put aside, ie, 3. Now we need to figure out a number 6_ × _ = 89 The number in the blanks must be same In this case, 63×3=89, so we put another 3 aside So this makes √1089=33

[@PixelionRules]

@Dark As for what you had asked, consider 10201 (we all know it's a square of 101) Let's try solving this. We pair 1, 02 and 01 First number is 1, which is equal to 1², so we put 1 aside We will add 1+1=2 However, now there is no number to satisfy this 2_×_=02, so we put 0 in the blanks Now we put 0 aside Now we bring 20+0 down (we do not add the whole number, we only add the blank space number from the second step) That makes its 20_×_=201 (because we could not do it, we bring down two too) Now we know 201×1=201, so there goes another 1 and we put it aside That makes √10201=101

[@PixelionRules]

@Dark np :)

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@cuckyoin3471]

Yess same heree

[@TopWorldTalentHD]

Thanks!

[@maybefunny3196]

Ur welcome

[@TopWorldTalentHD]

@@maybefunny3196 😂😂😂

[@CoronaLisaa]

@@cottoncandycloudsrobloxedits bc they donated 2 dollars….. duh

[@TopWorldTalentHD]

@@CoronaLisaa It was a test😂😂Next time I try $5 and see how many likes I can get.

[@sy-2]

@@TopWorldTalentHD then you're basically a verified bot jk

[@valquirit7606]

I already knew the method for cubic roots, though i had no idea it could be extended to square roots. Really nice piece of knowledge

[@shootboomzap]

As someone who loves math but was born in an era of calculators, I was never taught this method at school. Still, this is a really cool thing to learn and know

[@spookysomeone]

yeah! i always found it really frustrating when teachers just offered the guess-and-check method. i wanted to know how to actually do it, but they never gave an answer.

[@mohdmeheraj]

@@spookysomeone vedic mathematics lol

[@maheshpatil-yl7pu]

Wow ur a legend that u love math😂😂😂😂😂👏🏻👏🏻🙌🏻🙌🏻🙌🏻👏🏻👏🏻👏🏻

[@user-cz9ou4ue7v]

As another math lover, I'm torn between being happy and sad that in our country, majority exams don't allow calculators

[@Robi2009]

I don't know what's more amazing: this method or fact we have MIT admission questions from nearly 150 years ago 🤔

[@anandk9220]

Just for info that I'm an Indian, IB/IGCSE And Indian Curriculum Math Teacher by profession. I don't know what this person has said in the video. Here's the best trick : TO FIND PERFECT SQUARE, CUBE OR Nth POWER OF ANY NUMBER : Just split the number into TWO parts in terms of place value, assume first part as A & second as B, and then use (A + B)^2 expansion. Example - 83 = 80 + 3 A = 80, B = 3 So, 83^2 = (80 + 3)^2 = 80^2 + 2 × 80 × 3 + 3^2 = 6400 + 480 + 9 = 6889 Similarly, 137^2 = (130 + 7)^2 = 130^2 + 2 × 130 × 7 + 7^2 = 16900 + 1820 + 49 = 18769 Similarly it's possible to calculate cubes and higher powers of ANY number using the binomial expansion (using Pascal triangle coefficients). TO FIND SQUARE ROOT/ CUBE ROOT OF ANY PERFECT SQUARE/ CUBE : By the way, all those who don't know this, there is an amazing 2 to 5 second technique to find square root of any perfect square, preferably a smaller number. Note that every group of two digits from right (starting from unit's place) to left will contribute to ONE digit in the square root (You can append 0 to highest place value as and when needed to complete two-digit group). Example - Square Root of 57121 1. Focus on unit's place and analyze the unit's place of square root (either 1 or 9, as both 1×1 and 9×9 ends with 1) 2. Temporarily leave the LAST TWO digits and focus on the remaining part of number. (In this case 571) Now locate this remaining number between two perfect squares. (In this case, 571 lies between 529 = 23 squared and 576 = 24 squared) 3. Since 571 is closest to 576, the square root must be closer to 240. Hence, Square Root of 57121 = 239 All dear friends, in case you are or want to be better at calculations, I'd like to share an app with you. Do try the 'Math Tricks' app by Antoni Ion from Google Play Store. Extremely good brains can try 'To The Bitter End' mode wherein they even ask 1885 squared and stuff at higher levels. [ Note : I tried 'To The Bitter End' mode many times and after reaching 163 to 165 levels, I accidentally pressed back button mostly everytime to wash away my hardwork. Finally with tons of patience, I strongly fought for 4 straight hours or more and completed 204 levels and then happily declared my calculation innings and stopped there ! ] 😂😄 You may also try Hard Math Game by marcin.magician from Google Play Store and reply your experience. In case you're interested in solving Math puzzles, do visit contestcen.com and go to Site Map (with various puzzle pages like Digits, Easy Math, Tough, Harder, Geometry, Convergence, Primes, Squares and Powers etc.) Highly skilled and interested minds, do visit contestcen.com/geom.htm and try the following questions - 1. Circles in a Square 2. 4 Tangents 3. 5 Spheres 4. TetraSpheres Thank you. Love you all. 😙😙😙

[@bhavishyasharma7834]

MIT,Oxford, Harvard, all these are very old universities, 200 or 300 years ago

[@Robi2009]

@@bhavishyasharma7834 duh, I know, but I didn't realize they keep their records for so long Btw Oxford is way older than that, it's over 800 y old.

[@bobon123]

@@Robi2009 And not the oldest either, the first University is Bologna. And we have tests to become civil servant in China (the Imperial examination) from almost 2000 years ago.

[@Manior-ep9vn]

This is actually the most helpful video on the square root i've ever seen. Thank you so much!

[@kaylansaravanapavan7718]

That is actually so fascinating. I never would have thought that

[@guessundheit6494]

This can also be solved with remembering landmarks. 841 is nearly 900 (30^2). 900-841=59, approximately 30x2, so 29^2. 1024 (32^2) is close to 1156. 1156-1024=132, approximately 4x32, thus 1156=34^2. 3969 is nearly 4000. (400x10)^0.5=20x3.16=63. 16384? Who doesn't know their binary? (1600x10)^0.5=40x3.16=126. 16384 is larger than 16000, so the last digit is 8, or 128. 39304? 3^3=27, and 11^3=1331. 33^3=35937. 39304 ends in 4, so it's 34. My method looks more complicated than the video's example, but this can apply to finding ~any~ cube root, not just exact roots.

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@thanmayee.s8244]

Awesome, I understood it!!😊👍

[@Flatner3]

3:10 actually made me say "Ayo?" out loud.

[@MariaHernandez-bj3xe]

Love how you closed at the end with marvelous enlightenment.

[@IstanaghVlandis]

This is an amazing method to calculate square roots and cube roots! Great video!

[@Arob4343]

One of my favorite videos, that you’ve made. If I was still in school, this would be incredibly useful. But now, it’s just really cool to know

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@p.zansei3280]

Presh you never cease to amaze me with the logic videos, but learning shorthands like these blew my mind. Please teach more techniques like these for math and logic!

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@lEvElsh]

I genuinely thank you for teaching me this method, old, but gold. It also encourages me to learn math😊

[@Sith_Kermit]

Dude I did this in my math class and the kid that sat next to me called me a human calculator for the rest of the year😂

[@concretemathematics8146]

It’s crazy how easy to solve any square root problem (even cube root problem) with this easy approach. Thumbs up and my greatest salute to all the mathematicians from old days.

[@JuniorDjjrMixMods]

"any", it was said ONLY perfect squares. Only 10% of the numbers from 0 to 99 are perfect squares, only 5% from 100 to 199 etc. It works for just a few numbers.

[@37rainman]

Sorry, but obviously it is a totally useless trick. Might be useful for a 7 year old to impress a not to bright mother for around 30 minutes maybe

[@nathanmays7926]

5:59 “wow” Pretty much sums up this video.

[@themakeroffun9451]

i watched this video about 7-8 months ago and forgot about it but not the trick so I used to think I developed this trick until today I came across the video again, thanks for saving me a lot of time in highschool

[@kiyoko1]

this is the most helpful math videos i have seen in a VERY long time

[@KCKingcollin]

Some people laugh at me for learning things online, but the way I see it, the internet is an infinite encyclopedia of knowledge that you could never get from a single book, thank you, for teaching me something I never would have thought to learn, but I can tell will be extremely useful going forward

[@chadd990]

the only problem with learning things online is that anyone anywhere can post anything anytime they want. You do have to do a little bit more research to make sure that their claims are true. other than that, yes the internet is a gold mine of information.

[@KCKingcollin]

@@chadd990 true that definitely is an important take away

[@Vadoseharpy3025]

I actually use both of this methods and they are phenomenal and can help you in a pinch. You can also do this with other odd roots like, 5, 7, 9 and so forth. Even numbers are harder especially 4th root since they have numbers that end with either 6 or 1 and finding a way to differentiate that with other numbers are hard.

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@make-a-wish2224]

Why can't i get the square root of 1091 with This number??

[@patriciamaher597]

@@make-a-wish2224 Because 1091 is not a perfect square

[@miantony6493]

I recommend this maths problem . This guy is crazy applied a method that I have seen before in KZbin . kzbin.info/www/bejne/sGOyqol_f9-hftk

[@archimedesmaid3602]

@@patriciamaher597 And that is why this method is worthless, and why it isnt taught in schools. You can, in the time it took to watch this vid, learn a simple method to calc the sqrt of 1091 to any accuracy you might desire What is the sqrt of 10? How easy is it to multiply that number by 20? How easy is it to add a single digit to that result? How easy is it to multiply that result by the same single digit? How easy is it to subtract that result from the current remainder? Can you handle this?

[@PythonicSerpent]

This is the BEST video on square roots and cube roots I have ever seen and this will help me with highschool math so much

[@TheWeirdWorldOfVideoGames]

Brilliant. Thanks for the explanation, Presh.

[@kirillzakharov7336]

One thing to note is that each time, the difference between two following perfect squares increases by two. And it's always odd. 0 1 4 9 16 25 36 etc. And this continues even from 729 (27^2), to 784 (28^2). The difference between them is 55. Then, to from 784 to 841 (29^2), the difference is 57.

[@molibdenum]

This is true, because the difference n^2 - (n - 1)^2 = 2n - 1, and the difference (n + 1)^2 - n^2 = 2n + 1, so the increase = (2n + 1) - (2n - 1) = 2. And the odd part can be seen from the fact that 2n ± 1 is always odd.

[@kirillzakharov7336]

@Zeniat Haroun and the difference between perfect cubes always increases by 6

[@furkanbekgoz5257]

I know it's a bit late but i wanted to comment. Your method is basically (x+1)*(x-1) which is x^2 - 1. It also helps at pythagorean problems. It made me feel very clever back then I was at middle school but now im at university and I lost all interest with math :( ...

[@kirillzakharov7336]

@@furkanbekgoz5257 damn I first figured that out in freshman year. nice

[@kwilson5832]

I think it's worth considering why this is true. Imagine drawing a 3 x 3 square on a piece of paper. There are now 9 small squares contained in this 3x3 grid. If you want to change it to a 4x4 grid, you would add four squares to the right of the grid (three to the right of the three already in the grid, and one below), then three more squares underneath to complete the square. So in total, you've added 7 squares. If you want to extend it again, you would add five squares to the right (that's one more than before) and four underneath (that's also one more than before). You're always adding an odd number and an even number of squares, so the total squares added is odd, and two more squares than you added the previous time.

[@johnmcclain3887]

I've had problems in math all my life, being dyslexic, but have worked in technology despite the problems. This has been a very interesting exercise in square and cube roots, I wish I'd learned in my days in school so long ago. Thanks for showing this means.

[@archimedesmaid3602]

You wernt taught this in school, because the ability to calc the sqrt and cuberoot of perfect squares and cubes cannot be used for anything real.

[@LunarMoth]

@@archimedesmaid3602 Depends on your area

[@grookes4040]

This is really helpful, thank you. I've been stuck with square roots for a while

[@deepasshetty5712]

This video became helpful to me . As i am in 7th in "Triangles and its properties" lesson our NCERT math text book gave examples to find square number but they didn't gave examples to find square root number so i couldn't understand how to find ans using Pythagoras theorem. Then i saw ur video which gave many such examples which taught me very understandable and cleared my doubts. Ur speaking is also very clear and understandable.

[@stefanodigarbo4735]

This is superb. I'd love to see the demonstration of the method. Could you make a video for that?

[@jonbonda1917]

My high school math teacher showed me a quick solution by the graphical method. Similar to squares or cubes of # up to 16 in a circle. Reminds me of the Fibonacci circular graph. Of course there's limitations to numbers that are more than 6 digits as you have to scale up the method but it's consistent with the same method of this video. It was more of a quick solution as you have to display in trigonometric values for the square or cube roots as well as the max/min values very quickly. So similar method but displayed in a circular graph and then expressed in degrees of angles.

[@TalkToDaddy]

Thank you so much!!! This video helped me alot. I was having alot of problem in finding roots but with the help of your explanation and this trick i am now confident in easily finding roots. Appreciate your hardwork 😊❤

[@oklandon09]

This was extraordinarily helpful, thanks!

[@akshataashok4222]

Thanks a lot for this video 📹 the last day before the exam it helped me so much .

[@t5zeus554]

Wow this is so helpful I shared it with all my friends it will make a large difference for my 10th board examination

[@Love.every.bit.of.life123]

THANK YOU SO MUCH!!!! I legit had a Maths Assessment tomorrow and I knew everything about algebra and etc but I was really stuck with this and now in this way, I know how to do them, I really appreciate it😄💖✋🙏

[@Reach_Assasin]

Wow! This is just amazing. Thank you so much for teaching this to us! You earned yourself a subscribe.

[@jameskelly4873]

This was actually pretty informative, thank you so much.

[@37rainman]

You will never make any use of this useless information though

[@Ma-ol6pp]

@@37rainman it will help me a lot in school

[@37rainman]

@@Ma-ol6pp So your school has tests where they declare beforehand: "Anytime you need to find a square root of a number in this test, the number will be a perfect square". Yes??? Or maybe in your country, every single time any student encounters a number she needs to find the sqrt of in any test, that number will be a perfect square So, lets see.............. You have a test question, and in the test you cannot use calculators, "What is the dimension of a square which contains 1000 square feet?" You cannot give the answer beyond saying "somewhere between 30 and 40 feet". Only in India ..................... Wouldnt it be better to just learn a method to find sqrts of ANY number to ANY accuracy desired, and very quickly, since you are apparently interested in this subject? It will take you about 1 minute to learn it

[@ziadjsd1088]

​@@37rainman exactly

[@SilvinaLisboa]

Thank you for the video and the class of History!!! That was awesome!

[@jrwise100]

Thank you for posting this!!

[@mouradbelkas598]

Thank you. You are a great math professor. Excellent explanation and good choice of examples..

[@RADHEY-KRISHNA]

We use long division type method. That's better for even non-perfect squares. Btw, Great Video! Thanks for sharing.

[@chengshengway]

Yes.

[@bagelnine9]

Please explain how it works. Can it approximate roots? Can it work for other root bases?

[@RADHEY-KRISHNA]

• Step 1 : Separate the digits by taking commas from right to left once in two digits. Ex. 98087 = 09,80,87 Ex. 108087 = 10,80,87 • Step 2 : Write the no. which has the square closest to (and less than) the first two digits before comma. __3_________ 3 | 10,80,87 | -09 | = 01 | • Step 3 : Move down the digits in pair. __3_________ 3 | 10,80,87 | -09 | = 01 80 | • Step 4 : Add the same digit on left side that you've written last above. __3_________ 3 | 10,80,87 +3 | -09 =6 | = 01 80 • Step 5 : Now, you have to do like this, 61×1, 62×2,....and find a no. that is less that or equal to the no. written on r.h.s. In this case, we take 62×2=124 (since 63×3 = 186>180) __3 2________ 3 | 10,80,87 +3 | -09 =62 | = 01 80 | - 0124 | = 56 • Step 6 : Now copy next two digits. __3 2________ 3 | 10,80,87 +3 | -09 =62 | = 01, 80 | - 0124 | = 56,87 • Step 7 : On l.h.s, we must add the digit, we wrote last. Like here, it would be 62+2, and not 62+62 __3 2________ 3 | 10,80,87 +3 | -09 =62 | = 01, 80 +2 | - 01 24 = 64 | = 56,87 • Step 8 : Now, do the same, 641×1, 642×2....here, we get 648×8= 5184 < 5687 __3_2_8_______ 3 | 10,80,87 +3 | -09 = 62 | = 01, 80 +2 | - 01 24 = 648 | = 56,87 | - 51 84 | = 05 03 • Step 9 : After this, put a point above and add two zeroes to get 50300 and repeat the same. If you would've got, say 5000 only and on the l.h.s, 648+8 = 656, then we see 656x × x > 5000, then above, put a 0 to get 328.0... below put two zeroes, 5000,00 and on the l.h.s one zero, 6560, and continue 6560x × x.... Hope it helps! It doesn't approximate, but gives exact. It might work for cube roots too, but is a bit complicated and I actually, don't know, would prefer prime factorisation to approximate.

[@surekhasangale8907]

@@RADHEY-KRISHNA there's no way you didn't copy paste that

[@RADHEY-KRISHNA]

There's a way, I typed. Honestly, if you believe. Have a great day!

[@rminitials]

Very interesting method. Actually quite well. Thank you.

[@mxngokiwi]

This is the method to go! I've just discovered this video and it has saved me so much time in math. Thanks!

[@rupankitamukherjee2639]

Really helpful video,these tricks help students(like me)so much! Thanks for posting...and, surely, I will honestly confess that though I knew Aryabhatta discovered the 'Zero', I didn't know that the entire numeral system has its origin in Indian histroy! Wow,feels awesome learning such informative facts.I wonder how a thing this big about my country skipped me.

[@kashyap_0-0_]

Indians themself are too occupied with learning foreign teachings and discoveries by foreign scientists, our school syllabus tends to ignore a lot of geniuses (who didn't "register" themself a patent somewhere in west) It's really sad

[@rupankitamukherjee2639]

@@kashyap_0-0_ You are sooo right🙁

[@shreykumar4775]

Thank you for this, im a 9th grader and it is tedious to find square roots with the traditional methods, this is much faster and efficient, truly thanks 👍

[@joshwajos4930]

@Darkthe long division method

[@aryan_wanve]

@@joshwajos4930 ahh, that sucks

[@37rainman]

@Dark Lol, the long division method can be used to find the sqrt of ANY number to 2 or 3 digit accuracy , in seconds. While this method is really useless for anything at all. (When in your life do you ever run into calculations where you know beforehand that the number in question is a perfect square?). I just did the sqrt of 528941 to 3 digits accuracy. Timed myself. It took all of 40 seconds I didnt even think about whether it might be a perfect square or not. And I could have continued to 6 digits or whatever in very little time. It is just a long division process where (for each iteration) the divisor is generated by multiplying your current answer by 20. You could have leaned it in less time than it took to watch this goofy vid SO incredibly difficult, correct??

[@donnafletcher5386]

Great presentation. Loved the history too.

[@anonim1t]

Simply AMAZING! Loved it ❤️

[@aussietaipan8700]

This was really cool and can be further built upon to suit other minds.

[@jxyden95]

Only 1800s kids remember

[@nightopia.1981]

same

[@AndyChanCubing]

This is the best video ever! This makes calculating square roots so much easier. Thank you!

[@archimedesmaid3602]

Ok, then, what is the sqrt of 136? If you say "i dont know because that isnt a perfect square", then you really haven't learned to do sqrts.

[@vivek3496]

brother, it is a super, legendary, awesome, god-level, less for words to express video helping students with competitive exams I will share it to at least 50 people you plz keep on making this type of videos

[@x_Infinite]

Thanks, will really help with studying algebra.

[@verypanda1801]

I’d recommend using a “factor tree” if you are studying algebra. The method in the video is really neat but in my opinion if you are new to the topic you should go with factor trees (or similar methods to factor trees).

[@LukaGalactica]

@@verypanda1801 agreed

[@TheGodQuac]

@@verypanda1801 bro said algebra not basic maths

[@LukaGalactica]

@@TheGodQuac there are still basic mathematics in algebra

[@riskacendana8085]

Thanks a lot, this is helpful!

[@TolaseRichard]

hay pal

[@olegmoki]

pal hay

[@andrewboys2547]

This is going to help so much in my math class. thanks for making this video!

[@die_geilesten]

This video is a lifesaver. I'm subscribing.❤️

[@buckbuster69]

One more method that I like to use is (a^2+b/2a) where a is the nearest perfect root and b is the number itself. It helps when the square root is in decimal for example if we take the number 66 the nearest perfect root number is 64 then (64+66)/(2*8) which would give us 8.125

[@robinbailey7460]

you need the bracket correctly written in your general expression. (a^2+b)/2a Your actual calculation used the correct priority system - not what you wrote as the general expression. I assume it was a typo.

[@varun9954]

Oh my god...this is just awesome and it's saving 2 to 5 minutes of calculations of mine and now I can solve problems more efficiently. Thanks to you!✌️✌️❣️❣️

[@beeble2003]

What problem does this let you solve efficiently? I can't think of a single situation where I've been given a number which is guaranteed to be a perfect square, _and_ I've needed to take the square root of it, _and_ I've not had a calculator or computer available.

[@varun9954]

@@beeble2003 Oh dear, I didn't mean to make you feel bad but the competition for which I'm preparing has quite a few big perfect square roots in between the solutions, so, this trick really helped me a lot. I hope I cleared your doubt.

[@beeble2003]

@@varun9954 Oh, OK. So the situation is an artificial one but it is, nonetheless, a thing that's useful to you.

[@Marianojoey]

This method is AWESOME!!!! Thanks for sharing. :D

[@snehaarora8016]

Congrats dude u successfully got a new subscriber. Btw i loved ur video

[@y2ksw1]

As a kid, I worked out any square root with my own invented algorithm, at that time. Later I found out, it was called "by approximation". As a Software engineer I have used this method at all times for time critical calculations with best results.

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@izzmus]

There is a slightly easier (for me, anyway) method to determine which of the two options for ones digit of the square root is correct: If the thousands/hundreds digits of the square are closer to the next lowest square or the next highest square. (if it is 11, 11 is closer to 9 than to 16, so the root's ones digit will be the lower of the two numbers)

[@seanleith5312]

Presh Talkwalkar, the most depressing name I have ever heard.

[@talentic6569]

@@seanleith5312 ?

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@dragonizegamingind1121]

@@talentic6569 lol

[@37rainman]

What are you talking about?? It doesnt matter whether 9 is closer to 11 than 16 is. Take the sqrt of the number 15 instead. Obviously 15 is closer to 16 than 9. But just as obviously the first digit of the sqrt of 15 must be 3, not 4 Correct??

[@gumarks_]

Such an interesting and simple method!!

[@isaaclee6171]

Thank you so much for teaching me the easier way to calculate! This help a lot.

[@shinjinibahadur4460]

Very helpful, thanks a lot!

[@TolaseRichard]

b

[@Virtualleeeeee]

I can tell this is gonna be useful on my homework

[@sassymeyou]

this is really helpful ! thanks !!

[@Spodermin87]

Thanks a lot for this! I have been struggling to work out complex square roots in my head (e.g: 2989)! This video, however, helped me. Thank you so much for this! 😃

[@itsmejed5181]

But 2989 isnt a perfect square

[@tiagosoares3959]

Love it!!!!

[@crazyshauny5012]

I may not be good at math but this helped me quite a bit. Thank you :)

[@mosesmuchina1308]

Amazing. Excited from Nairobi Kenya.

[@Dis_Is_Warrior]

Incredible video and a lot of information ❤❤❤❤

[@labscience8271]

1:24 10^2 ends with 0 as well, so we might consider this as well...

[@GeeWhiz1520]

This is good, I’ve known this technique for a while, however a 1st order taylor approximation has been more useful with little error for square roots. Nice video though.

[@rubixgaming2179]

thank you so much this was SO HELPFUL

[@Badkitty24]

Thank you for this. Seriously. I worked in retail for 10years and i could ALWAYS add up totals in my head and figure out change, BEFORE someone was able to type all the numbers in the computer. I have also shown people how fast i can add by having them write down 2-5 sets of 2-4 digits of numbers...and i'd have them added before they could enter into a calculator. I can SEE and hold numbers in my head, repeat numbers verbally in my head and visual look at numbers all at the same time while i'm adding and rounding numbers up. I never had to do subtraction much so i'm not as fast, but i can do it. This will be another trick for me :D I just have to remember those sets of numbers.

[@TheRealBobHickman]

16384 is easy if you're a computer programmer.

[@sharadkumarsingh4802]

Yeah I too find it very easy to operate on base 2 numbers

[@aurexify]

I'm not a computer progammer but I have memorized all the powers of two up to the 24th power (16 777 216).

[@trueimaliar]

This was extremely satisfying to watch.

[@siddhidaga4845]

amazing technique 👌helped me a lot

[@1a1u0g9t4s2u]

This is a really nice way to solve for sq roots and cube roots. Like multiplication tables when I was a child, this would be nice to practice for today's students. My gut feeling is...if practiced enough with this method one could be fast but not as fast with this method as it would take to enter it into a calculator and would impress your friends.

[@varaprasad9]

kzbin.info/www/bejne/on22c6CAZZihnrM

[@37rainman]

You will never in your life be able to do anything practical with this trick. It is totally useless information

[@user-fb2qr4ru6i]

Eu gosto disso! Boa explicação detalhada!

[@Mdt_01]

Nice Guy! Great job!🤓Thanx a lot for this

[@mateirusu7968]

this is so helpful!!! thank you so much!

[@jayeshsolankiii]

This method is of Vedic mathematics teach us in 9th class. This is an ancient India method. 🇮🇳🇮🇳

[@jatinchawla4236]

Right bro

[@joedi]

This is Vedic Math. vilokanam (squareroot) & ekadhikena purvena (squares)

[@yashghosh1316]

Sir what we do in 6 digits number

[@shubhamshinde4502]

Thank you for sharing this with us.

[@khushaljogur]

This saves so much time. Thank you so much!

[@AdityaSingh-uh9lq]

Proud of my country 🇮🇳🇮🇳

[@divishachauhan3026]

I am seriously not kidding but it's bean 4 years and each year I search on google and watch this video 😂😂😅

[@manarmansour3670]

But isn’t the video before 8 months