Square root of ANY number instantly - shortcut math.

This math trick allows you to work out the square root of any number - NOT JUST PERFECT SQUARES - instantly. With decimals. With ease. Can you work faster than a calculator? With this tecmath trick you just might! The math shortcut magic is back!

[miabasile]

"I'll give you acouple seconds to work that out"
Me: Sweating
A 30 second add: "I got you"

[gangleweed]

So, now after 60+ years out of school I can finally calculate square roots mentally.

[grahammustoe]

The trick is actually based in calculus. It’s the Taylor series approximation using two terms for the square root function. Without reading through the hundreds of comments already made I’m sure several other people have probably mentioned this. Just shows you that calculus can be really useful!
What’s really neat is that if you use a Taylor series approximation with three terms, its even closer to the exact value of the square root.

[kessadecleene]

Honestly I stumbled across this while I was half drunk.😂😂 And I was somehow able to follow along and get them all right! I even kept the sheet to prove I get it! This taught me better than school did! Props to you mate! This is awesome!! I hated math but getting these answers right boosted the hell out of my confidence!!

[mabimabi]

This guy is like the backdoor dealer of mathematics

[-Minuano-]

Math is fun when your “life” doesn’t depend on it. Aka grades.

Edit: 13k likes!? Holy... Thank you, everyone.
Also, there's a fight in the comment section lmfao. I'm very sorry I caused this chaos.

[parisgreen]

This is great! I always thought I was 'bad at math' until I took a VERY basic course in my 40s and discovered that, not only can I do math well enough to get by, but it's actually fun.

Your video presentation is super clear and friendly. I was able to do all the problems the first time through; going to check out your other videos now. Thank you!

[peachycloudz]

This is actually perfect for me, I recently learned about square roots this year and this will be very useful for the years to come. Thank you

[Smallpriest]

How engineers find square roots instantly:
Step 1: find the closest perfect square
Done

[MineSweeper-bgun]

I can't believe how much an 8 minute video expanded my brain by

[SeventhFromAdam]

I was never really good at math. Learning this method actually piqued my interest with numbers. I enjoyed the challenge. Thank you!

[ernjdasdd]

Well to be technical, the square root would be much easier when comparing the remainder number to the next closest perfect square. So 36 squared is 6, but we have 3 left over from the 39, the next closest square is 49, the difference betwen 36 and 49 is 13, so we have our remainder over the difference. The square root of 39 is 6 and 3/13ths.

[bravoklo]

Never expected Bruce from Finding Nemo to be teaching me math tricks at 3am yet here I am

[Birju_Maharaj]

Note : this trick is actually quite good in competitive exams where approximations work, , , thanks

[ThePiMan]

Very nice and helpful sir! This is very useful for estimating radicals. Thanks again!

[dougdimmedome]

I never knew that being taught math by an Australian was something I needed in my life.

[publiusii]

This is actually impressively precise. For my own enjoyment I wrote a script that used this method for the root of every number up to a million. The highest margin of error was a little over a fifth for the root of three. With precision trending to increase proportional to the size of the number. By the time you reach thirty the number is accurate to +/-0.1

[uf]

Here's how this works algebraically:

Let √c = a + b, where a represents the whole number component of the answer, a ∈ Z, and b represents the decimal component, 0 < b < 1
c = (a + b)²
c = a² + 2ab + b²

Now solve for b:
2ab = c - a² - b²
b = (c - a² - b²)/2a

b² (the decimal component squared) will be very small, so we can ignore it
therefore, b ≈ (c - a²)/2a
in other words, b ≈ the original number, c, minus the nearest perfect square below it (the whole number component squared), all over 2a: which is the formula given in the video for working out the non-whole number part of the answer

e.g. √27 = 5 +b
27 = (5 + b)²
27 = 25 + 10b + b²

10b = 27 - 25 - b²
b = (27 - 25 - b²)/10
b ≈ (27 - 25)/10
b ≈ 0.2
√27 ≈ 5 + 0.2 = 5.2

As further proof, the approximate answer will always be out from the actual answer by a margin of b²/2a:
5.2 - 5.196... = (0.196...)²/10

[sofusflorjensen]

On the one with the square root of 138, I actually tried using 12 instead of 11, giving me the number 144. Here I subtracted the 6 and divided it with the 12 doubled, 24, boiling down to 0, 25. But since I am under the actual value instead of over, I simply subtract the 0, 25 from my root 12 instead of adding it on top, as he does with 11 in the video.
Hope this made sense, and might help someone, have a nice day if you find this

[wild_lee_coyote]

Reminds me of Richard Feynman when an abacus salesman challenged him to a math contest. Ended in a square root contest. Feynman won because the number was close to a perfect square and he could quickly refine the number. That and doing square roots on an abacus is very labor intensive.