Solution - Simplifying square roots

Simplify :  sqrt(27000) 

Factor 27000 into its prime factors
           27000 = 2³ • 3³ • 5³ 

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 :
           900 = 2² • 3² • 5² 

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 :
           30 = 2 • 3 • 5 

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

Simplified Root :