Solution - Simplifying square roots

Simplify :  sqrt(300000) 

Factor 300000 into its prime factors
           300000 = 2⁵ • 3 • 5⁵ 

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 :
           10000 = 2⁴ • 5⁴ 

Factors which will remain inside the root are :
           30 = 2 • 3 • 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 :
           100 = 2² • 5² 

The simplified SQRT looks like this:
         100 • sqrt (30)  

Simplified Root :