Maths Tricks

Square Root of Imperfect Square

Hey here i am going to share a trick on finding out square root of imperfect squares. First of all we should now what are imperfect squares.

Imperfect squares are the number whose square root are not integers like 2,3 etc whereas number like 4,9,16,25 are perfect square because there square roots are 2,3,4,5 respectively.

Method

So lets look at the simplest method that can be applied for finding square root of imperfect squares. You only need to remember following formula.

x±y = √x ± y/2√x

Lets understand above formula of finding square root using some example

Example: √17

First Split 17 such that you can find the nearest perfect square in our case we can split it us follows

16+1So here comparing with formula x=16 and y=1 putting it in formula we get

16 + 1/2√16

On simplifying we will get it as 4+1/(2*4)

that can be written as 4+1/8 ie., 4+0.125 = 4.125

Hence Sqrt of 17 comes out to be 4.125(approx)

These is more easier method as compared to traditional long division method of finding square root of imperfect squares. So give it a try and if you find out any problem the please comment below.

Shubham Lashkan

Myself Shubham an computer science engineer with lots of dream having an unseen attitude with lots of thoughts

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Myself Shubham an computer science engineer with lots of dream having an unseen attitude with lots of thoughts
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4 thoughts on “Square Root of Imperfect Square”

1. Geetika Tiwari says:

If we put X=1 and y=16 then answer will be changed …so is there any concept about x and y ?

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2. Ritesh vaishnav says:

Really,easily solve this method of mathematics.