Question

simplify √243 a^10 b^5 c^10

Answer 1

Factor 243 into its prime factors
           243 = 35 

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 :
           81 = 34 

Factors which will remain inside the root are :
           3 = 3 

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
           9 = 32 

At the end of this step the partly simplified SQRT looks like this: 
         9 • sqrt (3a10b5c10)