Solution - Simplifying square roots

Simplify :  sqrt(175) 

Factor 175 into its prime factors
           175 = 5² • 7 

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 :
           25 = 5² 

Factors which will remain inside the root are :
           7 = 7 

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 :
           5 = 5 

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

Simplified Root :