Solution - Simplifying square roots

Simplify :  sqrt(144) 

Factor 144 into its prime factors
           144 = 2⁴ • 3² 

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 :
           144 = 2⁴ • 3² 

No factors remain inside the root !!

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 :
           12 = 2² • 3 

The simplified SQRT looks like this:
         12  

Simplified Root :