Name: Square Root of Any Number in 3 seconds - Crazy Math Trick
Uploaded: 2026-01-06T02:51:24.000Z
Duration: 5 min 44 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Gerund

What if I ask you to quickly tell me in five seconds what will be the value of square root of 81 without using a calculator?

Future simple

You will laugh at me and say it doesn't require a calculator or even five seconds.

Modal verbs - A2

But now what if I ask you to find the square root of 87 without using a calculator and within 5 seconds you will be like, wait a second, it's not a perfect square.

And that's where things get tricky, right?

Today in this video I am going to show you an awesome trick to estimate square roots of even a number that is not a perfect square at a lightning fast speed.

However, at the end of this video I will show you that at some places you can.

You have to be careful while applying this trick.

Let us start with square root of 87 itself.

As a first step, you need to write the squares of all numbers from 1 to 10 like this.

Now just find a number whose square is just less than this value, which is 9 in this case.

So we know that our answer will be nine plus something and we need to find this something which will be a fraction.

Then subtract it with this squared number 81 to get 6 and write it in the numerator.

Then take this number nine and double it to get 18 and put it in the denominator.

This will become 1 over 3, which is roughly 0.33.

Actual value of the square root of 87 is 9.327, which is super duper close to our approximation.

First let us find a number whose square is just less than this value, which is 6 in this case.

So we know that our answer will be 6 plus a fraction.

Then take this number 39 and subtract it with this squared number 36 to get 3 and write it in the numerator.

Then take this number six and double it to get 12 and put it in the denominator.

This will become 1 over 4, which is roughly 0.25.

Actual value of the square root of 39 is 6.245, which is super duper close to our approximation.

Now find square root of 6964 is just less than 69 and thus it will be 8 plus a fraction which will be 69 minus 64 or 5 over 8 times 2 or 16 which is 8.3125 and the actual value is 8.307 which is very very close and super fast.

It will be 5 plus 27 minus 25 or 2 over 5 times 2 or 10 which is 5.2 and the actual value is 5.196.

Now let me show you where you have to be careful in order to use this trick.

Let us try to find the square root of 2 using this trick we get 1 plus 2 minus 1 or 1 over 1 times 2 or 1.5 which is definitely not very close to our answer as the actual value is 1.414.

So what to do now we will repeat it with this estimate of 1.5 its square is 2.25.

Write 1.5 plus 2 minus 2.25 will be minus 0.25 over 2 times 1.5 or 3.25 is also equal to 1 over 4 and this will be 1.5 minus 1 over 12 or 1.417 which is a more accurate approximation of the square root of 2.

But you know what, if you want a more accurate answer then keep on repeating this until you are satisfied.

I will definitely not take credit for finding this square root method instead this method was developed by the ancient Babylonians, one of the earliest known civilizations who lived in Mesopotamia or the modern day Iraq.

It was later rediscovered and generalized by Sir Isaac Newton in the 17th century as part of his Newton Raphson method which is an iterative approach to finding roots of a function F of x using this formula which involves calculus and it will be out of scope of this video to dive into its mathematical derivation.

Now if this video gets 20,000 likes then I will make another banger trick video like this one.

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Square Root of Any Number in 3 seconds - Crazy Math Trick

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