Solution - Simplifying square roots

Simplify :  sqrt(2000000) 

Factor 2000000 into its prime factors
           2000000 = 2⁷ • 5⁶ 

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 :
           1000000 = 2⁶ • 5⁶ 

Factors which will remain inside the root are :
           2 = 2 

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 :
           1000 = 2³ • 5³ 

The simplified SQRT looks like this:
         1000 • sqrt (2)  

Simplified Root :