Solution - Simplifying square roots

Simplify :  sqrt(1960) 

Factor 1960 into its prime factors
           1960 = 2³ • 5 • 7² 

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 :
           196 = 2² • 7² 

Factors which will remain inside the root are :
           10 = 2 • 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 :
           14 = 2 • 7 

The simplified SQRT looks like this:
         14 • sqrt (10)  

Simplified Root :