SOLUTION: How do you simplify √(1/(3x^3 y))? I know it is x^2 outside the radical with y and x inside the radical but I'm not sure what to do with the 1/3.

Algebra ->  Radicals -> SOLUTION: How do you simplify √(1/(3x^3 y))? I know it is x^2 outside the radical with y and x inside the radical but I'm not sure what to do with the 1/3.      Log On


   

Question 562751: How do you simplify √(1/(3x^3 y))?
I know it is x^2 outside the radical with y and x inside the radical but I'm not sure what to do with the 1/3.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%281%2F%283x%5E3y%29%29

You are to rationalize the denominator

To do that we make the denominator into a perfect square:

To become a square the 3 in the bottom needs to be multiplied by 3
To become a square the x³ in the bottom needs to be multiplied by x
To become a square the y in the bottom needs to be multiplied by y

So we multiply under the radical by the unit fraction  red%28%283xy%29%2F%283xy%29%29

 = sqrt%28%283xy%29%2F%289x%5E4y%5E2%29%29 = sqrt%283xy%29%2F%28sqrt%289x%5E4y%5E2%29%29 = sqrt%283xy%29%2F%283x%5E2y%29

Edwin