Solution - Simplifying square roots

Simplify :  sqrt(7452) 

Factor 7452 into its prime factors
           7452 = 2² • 3⁴ • 23 

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 :
           324 = 2² • 3⁴ 

Factors which will remain inside the root are :
           23 = 23 

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 :
           18 = 2 • 3² 

The simplified SQRT looks like this:
         18 • sqrt (23)  

Simplified Root :