SOLUTION: Simplify by factoring. Assume that all expressions under the radical represent nonnegative numbers. 5√192x^7y^10 Please show me how to solve.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify by factoring. Assume that all expressions under the radical represent nonnegative numbers. 5√192x^7y^10 Please show me how to solve.      Log On


   

Question 252143: Simplify by factoring. Assume that all expressions under the radical represent nonnegative numbers.
5√192x^7y^10
Please show me how to solve.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First we must prime factorize 192 as 3*64. I want a prime number and a square number, ideally.
Second, I want my exponents to be as even as possible. Notice we have X^7. We can rewrite that as X^6*X^1. We want even numbers so when we take a square root, we divide them by 2.
Third we are read to evaluate: 5sqrt%283%2A64%2Ax%5E6%2Ax%5E1%2Ay%5E10%29 gives us
5*8*x^3*y^5*sqrt(3x), or simply
40x%5E3y%5E5sqrt%283x%29