Solution - Simplifying square roots

Simplify :  sqrt(62208) 

Factor 62208 into its prime factors
           62208 = 2⁸ • 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 :
           20736 = 2⁸ • 3⁴ 

Factors which will remain inside the root are :
           3 = 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 :
           144 = 2⁴ • 3² 

The simplified SQRT looks like this:
         144 • sqrt (3)  

Simplified Root :