SOLUTION: Rationalize the denominator is my weakness when there are variables as I get confused with knowing how to simplify and what is the better method. These are some questions I have th

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator is my weakness when there are variables as I get confused with knowing how to simplify and what is the better method. These are some questions I have th      Log On


   

Question 885778: Rationalize the denominator is my weakness when there are variables as I get confused with knowing how to simplify and what is the better method. These are some questions I have that I am stuck on:
sqrt(18x^2y)/sqrt(2y^3) (I think there might be factoring involved but I don't know how to factor in this type of problem)
forth root(2x)/forth root(3x^2) (I don't even know how to begin to solve this as it looks like it is in simplest form)
sqrt(63xy^3)/sqrt(7y) (I know that you have to multiple by sqrt(7y) but I'm not sure if the numerator will be sqrt(63xy^3*7y) or sqrt(441xy^4))
Also I am not too familiar with some of the rules involved with these types of problems and I have tried to research them but there is just to much variables and not enough explanations. If there could be explanations on the rules/methods used that would be great.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2818x%5E2y%29%2Fsqrt%282y%5E3%29
You can rewrite this,and do some cancleing
sqrt%28%2818x%5E2y%29%2F%282y%5E3%29%29 = sqrt%28%289x%5E2%29%2Fy%5E2%29%29
All the terms left are perfect squares, extract those and you have
%283x%29%2Fy
:
Same here, combine and cancel like terms
%284sqrt%282x%29%29%2F%284sqrt%283x%5E2%29%29 = 4sqrt%28%282x%29%2F%283x%5E2%29%29 = 4sqrt%282%2F%283x%29%29
:
Do the same as above but here you can extract the perfect squares
sqrt%2863xy%5E3%29%2Fsqrt%287y%29 = sqrt%28%2863xy%5E3%29%2F%287y%29%29 = sqrt%289xy%5E2%29 = 3y%2Asqrt%28x%29