# How to obtain the square root of imperfect square ?

You might have come across a number of questions in the competitive examinations, where you need to find a square root of a number. We have already discussed the shortcut on obtaining the square root of a number, if the number is a perfect square.

If the number is an imperfect square however, the conventional method is to go for division technique to obtain the square root of a number. However this technique takes a long time.

In this tutorial, we will discuss a  shortcut to obtain the approximate square root of an imperfect square.

Let’s say we need to calculate the square root of 95.

Let’s understand the steps:

Step 1 :  By looking at the number itself, we can guess, the square root of 95 lies between 9 and 10.

So, √95=9.__

Step 2 :  95 is 14 more than 92.  Add 14 divided by twice the integer part of the square root i.e., 9×2 = 18.

So, the approximate square root of 95 is 9.77 which is very close to 9.747 which is the actual square-root of 95.

Consider another example, Let’s say we need to calculate the square root of 150.

Step 1 :  The square root of 150 lies between 12 and 13.

So, √150=12.__

Step 2 :  150 is 6 more than 122.  Add 6 divided by twice the integer part of the square root i.e., 12×2 = 24.

So, the approximate square root of 150 is 12.25 which is very close to 12.247 which is the actual square-root of 150.

Using the same shortcut, can you obtain the square roots of

• 300
• 250
• 600
• 242

### Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

1. You are so interesting! I don’t suppose I’ve truly read something like that before. So nice to discover another person with some genuine thoughts on this subject. Really.. thanks for starting this up. This website is something that’s needed on the web, someone with a little originality!

2. Babita

There is typo error in step 2 of sq.root of 95 – 14 more than 81 should come instead of 92 & in step 2 of sq.root of 150 – 6 more than 144 should come instead of 122.

• kapil pursnani

Any shortcut for finding cube roots ?

• SHANKIT KUMAR

root 524 ka 22.91 aara h but 22.89 h real iss formula se approx to pta chlra h lkin exact value ni pta chri

• Its nice try to understand dear I like iy

3. kapil pursnani

Any shortcuts for finding cuberoots?

4. ParthaSarathi Rout

please calculate square root of 15 by this method. my result is not match the approximate result.

5. bharat kumar

sir please calculate the square root of 24 by this method ….am not getting the correct answer i.e the approximate result .

6. bharat kumar

sir please calculate the square root 24 by this method as my answer is not matching with the approximate value

7. JANANI

Thank u so much Sir…very useful trick for my bank exams….

8. subrat

What will be the square root of 288 as per this method?

9. Pomi

Sir please calculate square root of 24 by this method…

10. shruti

How we can find the square root of 2

11. dev

for root of 47 it is showing deviation.