Solution - Simplifying square roots

Simplify :  sqrt(24500) 

Factor 24500 into its prime factors
           24500 = 2² • 5³ • 7² 

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 :
           4900 = 2² • 5² • 7² 

Factors which will remain inside the root are :
           5 = 5 

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 :
           70 = 2 • 5 • 7 

The simplified SQRT looks like this:
         70 • sqrt (5)  

Simplified Root :