Solution - Simplifying square roots

Simplify :  sqrt(147) 

Factor 147 into its prime factors
           147 = 3 • 7² 

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 :
           49 = 7² 

Factors which will remain inside the root are :
           3 = 3 

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 :
           7 = 7 

The simplified SQRT looks like this:
         7 • sqrt (3)  

Simplified Root :