Solution - Simplifying square roots

Simplify :  sqrt(6500) 

Factor 6500 into its prime factors
           6500 = 2² • 5³ • 13 

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 :
           100 = 2² • 5² 

Factors which will remain inside the root are :
           65 = 5 • 13 

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 :
           10 = 2 • 5 

The simplified SQRT looks like this:
         10 • sqrt (65)  

Simplified Root :