Solution - Simplifying square roots

Simplify :  sqrt(31104) 

Factor 31104 into its prime factors
           31104 = 2⁷ • 3⁵ 

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 :
           5184 = 2⁶ • 3⁴ 

Factors which will remain inside the root are :
           6 = 2 • 3 

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 :
           72 = 2³ • 3² 

The simplified SQRT looks like this:
         72 • sqrt (6)  

Simplified Root :