Solution - Simplifying square roots

Simplify :  sqrt(72500) 

Factor 72500 into its prime factors
           72500 = 2² • 5⁴ • 29 

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 :
           2500 = 2² • 5⁴ 

Factors which will remain inside the root are :
           29 = 29 

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 :
           50 = 2 • 5² 

The simplified SQRT looks like this:
         50 • sqrt (29)  

Simplified Root :