Solution - Simplifying square roots

Simplify :  sqrt(72) 

Factor 72 into its prime factors
           72 = 2³ • 3² 

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :
           36 = 2² • 3² 

Factors which will remain inside the root are :
           2 = 2 

To complete the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
           6 = 2 • 3 

The simplified SQRT looks like this:
         6 • sqrt (2)  

Simplified Root :