Maths trick!

 Introduction 

Hey I just found out a new method to estimate or get an idea of square root of large numbers. Here's how it goes:-

As you all know root 2 is an irrational number that is it is not defined. Anyone who has studied upto 9th or 10th knows to locate the value of root 2 on a number line using Pythagoras theory which comes out as near as 1.4. If you input root two in the calculator you get 1.4142135624... and so on. 

The method

Now what I found was that the square root of every natural number can be written as the product of root 2. Take any number. For example 20,000 is the number you take. The root of 20,000 is irrational so it can't be found using prime factorisation. Using what I just found I could estimate that root 20,000 is exactly 100 times root 2(root 20,000 = 100 x 1.4142135624...). This is how I got it.

1. Divide the number by 2

So 20,000 ÷ 2 = 10,000

2. Then find the square root of the number obtained

Here it is 10,000 so it's square root is 100

3. Now just multiply that by root is

That's how I estimated 20,000 root to be 141.4......(1.4142135624 x 100 = 141.42135624...)

You can write the root of any number as the multiple of root 2

Try this out

The number we want root of is 9

9 ÷ 2 = 4.5

root 2 × root 4.5 = 3

Check this in your phone calculator

Another example

Number is 6

6÷2=3

root 6 = root 2 x root 3

Check root 2 × root 3 and root 6 in calculator. The results are same. I hope this trick comes in handy to just get an idea of the square root of not all but some large numbers.