Solution - Simplifying square roots

Simplify :  sqrt(5440000) 

Factor 5440000 into its prime factors
           5440000 = 2⁹ • 5⁴ • 17 

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 :
           160000 = 2⁸ • 5⁴ 

Factors which will remain inside the root are :
           34 = 2 • 17 

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 :
           400 = 2⁴ • 5² 

The simplified SQRT looks like this:
         400 • sqrt (34)  

Simplified Root :