Solution - Simplifying square roots

Simplify :  sqrt(512) 

Factor 512 into its prime factors
           512 = 2⁹ 

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 :
           256 = 2⁸ 

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 :
           16 = 2⁴ 

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

Simplified Root :