SOLUTION: I am working on homework and am having a hard time figuring this guy out. Can someone help me with the steps? If you know the answer and can show the steps and answer it would help

Algebra ->  Radicals -> SOLUTION: I am working on homework and am having a hard time figuring this guy out. Can someone help me with the steps? If you know the answer and can show the steps and answer it would help      Log On


   

Question 374550: I am working on homework and am having a hard time figuring this guy out. Can someone help me with the steps? If you know the answer and can show the steps and answer it would help me so much with the remainder of my work. Thank you.
√75p^3q^4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2875p%5E3q%5E4%29
When there are no fractions, like in this expression, all there is to simplifying square roots is to "remove" any perfect square factors of the radicand (the expression inside a radical is called the radicand). This radicand has several perfect square factors:
sqrt%2825%2A3%2Ap%5E2%2Ap%2A%28q%5E2%29%5E2%2Aq%29
I find it helps to use the Commutative Property to rearrange the order so that the perfect square factors are together (in front):
sqrt%2825%2Ap%5E2%2A%28q%5E2%29%5E2%2A3%2Ap%2Aq%29
Now we use a property of radicals, root%28a%2C+x%2Ay%29+=+root%28a%2C+x%29%2Aroot%28a%2C+y%29, to separate all the perfect square factors into their own square roots:
sqrt%2825%29%2Asqrt%28p%5E2%29%2Asqrt%28%28q%5E2%29%5E2%29%2Asqrt%283%2Ap%2Aq%29
Each of the square roots with a perfect square radicand can be simplified:
5%2Ap%2Aq%5E2%2Asqrt%283pq%29