Square Root of Any Number in 3 seconds Crazy Math Trick

What if ask you to quickly tell me in 5 seconds what will be the value of square roo of 81 without using calculator? You will laugh at me and say it doesn't require calculator or even 5 seconds. can answer it in 1 second. The answer is 9. But now what if ask you to find the square root of 87 without using calculator and within 5 seconds you will be like wait second it's not perfect square maybe around 9 something and that's where things get tricky right but don't worry today in this video am going to show you an awesome trick to estimate square roots of even number that is not perfect square at lightning fast speed. However, at the end of this video, will show you that at some places you have to be careful while applying this trick. So stay tuned. Let us start with square root of 87 itself. As first step, you need to write the squares of all numbers from 1 to 10 like this. Now just find number whose square is just less than this value, which is 9 in this case. So we know that our answer will be 9 + something and we need to find this something which will be fraction. To do that take this number 87 then subtract it with this squared number 81 to get six and write it in the numerator. Then take this number 9 and double it to get 18 and put it in the denominator. And that's it. This will become 1 over3 which is roughly.33. And our final answer is 9.33. Actual value of the square root of 87 is 9.327 which is super duper close to our approximation and it was faster than calculator. Now let us find the square root of 39. First let us find 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 fraction. Then take this number 39 and subtract it with this squared number 36 to get three and write it in the numerator. Then take this number six and double it to get 12 and put it in the denominator and that's it. This will become 1 / 4 which is roughly.25 and our final answer is 6.25. Actual value of the square root of 39 is 6.245 245 which is super duper close to our approximation and it was lightning fast. Now find square of 69. 64 is just less than 69 and thus it will be 8 + fraction which will be 69 - 64 or 5 over 8 * 2 or 16 which is 8.3125 and the actual value is 8307 which is very very close and super fast. Finally let us try square of 27. It will be 5 + 27 - 25 or 2 over 5 * 2 or 10 which is 5.2 and the actual value is 5.196. We are on fire. 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 two. Using this trick, we get 1 + 2 - 1 or 1 / 1 * 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 + 2 - 2.25 will be minus.25. 25 over 2 * 1.5 or 3.25 is also equal to 1 / 4 and this will be 1.5 - 1 / 12 or 1.417 which is more accurate approximation of the square roo of 2. But you know what? If you want more accurate answer, then keep on repeating this until you are satisfied. 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 Rafson method which is an iterative approach to finding roots of function ofx 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 will make another banger trick video like this one. If you enjoy my videos and want to support my channel, consider becoming Patreon as it helps me create more awesome content for you. Link is in the description. Also, you can support my channel by joining our community and becoming member. So, good