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.

 

Square_Root_of_a_numbers_1

 

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.

 

Square_Root_of_a_numbers1

 

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.

 

Square_Root_of_a_numbers_4

 

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.

 

Square_Root_of_a_numbers_3

 

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


Please contact me if some point in the tutorial is not clear. I would be glad to help.

 

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.

15 Comments

  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. 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.

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

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

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

Leave a Reply

Your email address will not be published. Required fields are marked *

Protected by WP Anti Spam