 Calculate Square Root Quickly Without Calculator

In this post, we will learn how to find the square root of numbers which are not perfect squares. The answer we get using this quick calculation technique gives us an approximate answer. However, approximation becomes a necessity when we are attempting questions in a competitive exam, where time is short and options are given. Most of the time we’re not required to get exact answer.

Prerequisite to Use this Method

The prerequisite of using this method is you should remember the squares of as many numbers as possible. I would recommend that one should memorize square of numbers from 1 to 50. Later this can be extended t0 100.

It will be a wonderful idea to first learn the short cut method of finding the square of any number. Other awesome short cut method which you should consider knowing before moving forward is Herons method of finding roots.

Square Root of any number which is not a Perfect Square

Square Root = Sq. Root of Nearest Perfect Square + {difference of the given number from the nearest perfect square / 2 x (Sq. Root of Nearest Perfect Square)}

For example,

Short cut to find the Square Root of 47.
Square Root of 47
= 7 + (47-49) / 2 x 7 (since the perfect square closest to 47 is 49; we will take square root of 49 i.e. 7 for calculations)
= 7 – 2/2×7
=7 – 1/7
= 6.86 (approx).

Short cut to find the Square Root of 174
Square Root of 174
= 13 + (174-169) / 2 x 13 (since the perfect square closest to 174 is 169; we will take square root of 169 i.e. 13 for calculations)
= 13 + 5 / 26
= 13.19 (approx).

Short cut to find the Square Root of 650
Square Root of 650
= 25 + (650-625) / 2 x 25 (since the perfect square closest to 650 is 625; we will take square root of 625 i.e. 25 for calculations)
= 25 + 25/50
= 25.50 (approx).

This method has got a limitation. You can use it only till the point you remember the square
If you’ve questions related to the above shortcut method or anything else related to mathematics, please post on QM’s Q & A platform. For anything else you can comment below. Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

7 thoughts to “Calculate Square Root Quickly Without Calculator”

1. joyce says:

sir can u pls post me some maths question 4 fp

2. anju says:

Sir can you plz post simplification topics vedic math formula for bank exam

1. Vineet Patawari says:

Anju, simplification topic in banking exam covers wide variety of calculation based questions. There are many tricks suggested for mental calculations and approximation to improve your calculation speed. You can check those tricks here – http://www.quickermaths.com/category/numbers-2/

3. pnkj says:

by this method answer is 20

1. Sweta says:

20+(399-400)/2*20 =20-1/40 =800-1/40 =799/40 =19.974

4. James Mason says:

Don’t you proofread anything you type? Your second example should be 13 + 5/26 instead of what you incorrectly posted as 13 + 5/13

1. admin says:

Hey James, I do proof read, but somehow this one skipped my attention. Thanks for pointing it out. I’ve made the change.

Vineet