Solution - Simplifying square roots

Simplify :  sqrt(45) 

Factor 45 into its prime factors
           45 = 3² • 5 

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 :
           9 = 3² 

Factors which will remain inside the root are :
           5 = 5 

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 :
           3 = 3 

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

Simplified Root :