### Short trick: Finding the square root of a non-Prefect Square Number:

Finding the Square root of a non-perfect square number with the help of the division method, we have already studied. As we know, the division method for finding the square root of a non-perfect square number takes a lot of time. In competition exams, It becomes very difficult to calculate it by division method. So, Here is a short trick of finding the square root of a non-perfect square number which will you help in getting the approximate value of the square root of a number within a few seconds.

This trick is very important for those students who are doing preparation for government job, SSC Exam (CGL, CHSL, MTS), IBPS Exam, UPTET, CTET, RRB Exam, and other competition exams. Here you can learn to find the square root of a non-perfect square number by learning only one simple equation. The solution of finding the square root number of a non-perfect square number is given here step by step. Let’s understand.
Firstly you have to learn the equation by which you can find square root. The equation is written below:

√(x±y) = √x ± y/(2√x)

Where, x = a perfect square number nearer to given number
y= a non-perfect square number nearer to it

### Example: √10=?

Step 1: Write 10 as 9+1, where 9 is a perfect square number nearer to it & 1 is a non-perfect square number nearer to it.
Put x=9 & y=1 in equation
√(x±y) = √x ± y/(2√x)
√(9+1) = √9 + 1/(2√9)
√(10 ) = 3+ 1/2×3
√(10 ) = 3+ 1/6
√(10 ) = 3+ 0.16
=3.16

### Example. √24=?

Step 1: Write 25 as 25-1, where 24 is a perfect square number nearer to it & 1 is a non perfect square number nearer to it.
Put x=25 & y=1 in equation
√(25-1) = √x ± y/(2√x)
√(25-1) = √25 – 1/(2√25)
√(24 ) = 5- 1/2×5
√(24 ) = 5- 1/10
√(24 ) = 5- 0.1
=4.9