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 9^{2}. 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 12^{2}. 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

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

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!

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.

Babita,

It is not 92, rather 9^2 and 122 -> 12^2 Hope this step is clear now

Any shortcut for finding cube roots ?

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

Any shortcuts for finding cuberoots?

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

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

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

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

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

Sir please calculate square root of 24 by this method…

How we can find the square root of 2

for root of 47 it is showing deviation.