Solution - Simplifying square roots

Simplify :  sqrt(164) 

Factor 164 into its prime factors
           164 = 2² • 41 

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 :
           4 = 2² 

Factors which will remain inside the root are :
           41 = 41 

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 :
           2 = 2 

The simplified SQRT looks like this:
         2 • sqrt (41)  

Simplified Root :