Solution - Simplifying square roots

Simplify :  sqrt(162) 

Factor 162 into its prime factors
           162 = 2 • 3⁴ 

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 :
           81 = 3⁴ 

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 :
           9 = 3² 

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

Simplified Root :