Square Root of a Number

Square Root of a Number. Before understanding what the square root of a number is, it is important to understand the meaning of root of a number. The root of a number is an equal factor of the number. For example, find the root of 25

First, we need to factor 25 :
25 = 1 × 25
25 = 5 × 5
The root of 25 is 5 because 5 is the equal factor for 25
We call 5 the square root of 25
The symbol : √


How to find the square root :
1. Trial and error. 
This is the most common way to resolve the matter of the square root and is suitable for children who have been smoothly calculate the square or multiplication. For example we will calculate the square  roots 64.
a.  So we try 5 × 5 = 25 (too small).
b.  Try the 9 × 9 = 81 (too big).
c.  Try the 7 × 7 = 49 (too small).
d.  Try the 8 × 8 = 64 (right).    
     So we get the square root of 64 is 8.

2.  Factorization. 
This method is quite attractive and practical.  For example, what is the root of 64    
64 => 2 × 32
     => 2 x 2 x 16
     = 4 × 16
Then the root of 64 => root 4 x root 16                            
    => 2 x 4 => 8
3. Approaching

This method is a variation and the continuation of trial and error. After practicing a few times, we will be very proficient in this way.For example, what is the root of 1681?    

The most sensible approach is 40 × 40 = 1600.     

Because the unit value of 1681 is 1 so the roots of the unit 1 or 9.     

In this case we choose 1.  So we get the answer 40 +1 = 41  ( 41 x 41 = 1681)