Question

How to calculate square root?

Answer 1

To calculate the square root, you can either use the √symbol on a calculator or you can manually find it using Prime Factorization. For non-perfect squares, Prime Factorization is the way to go. 
 
The first two steps work for solving large perfect squares as well.

1. Divide your number into perfect square factors.

2. Take the square roots of your perfect square factors. 

3. If your number doesn't factor perfectly, reduce your answer to simplest terms. 

4. If needed, estimate. In some cases if you have memorized some of the square roots, you can estimate where the number would be. 
ie.  $\sqrt{63}$       you know that $7^2 =49$ and $8^2 = 64$,  so you can estimate that the $\sqrt{63}$ would be between 7 and 8 but closer to 8.

5. Alternatively, reduce your number to its lowest common factors as your first step. Finding perfect square factors isn't necessary if you can easily determine a number's prime factors (factors that are also prime numbers).
ie.  $\sqrt{45}$
 =  $\sqrt{9*5}$
 = $\sqrt{3*3*5}$
 =   $3 \sqrt{5}$

Hope this helped!!!