Solution - Simplifying square roots

Simplify :  sqrt(592) 

Factor 592 into its prime factors
           592 = 2⁴ • 37 

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 :
           16 = 2⁴ 

Factors which will remain inside the root are :
           37 = 37 

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 :
           4 = 2² 

The simplified SQRT looks like this:
         4 • sqrt (37)  

Simplified Root :