SOLUTION: Looking for help with the following radical, which needs to be simplified. The book does NO help in explaining how to go about it. ^3sqrt -27y^18/81x^6 After scouring the inte

Algebra ->  Finance -> SOLUTION: Looking for help with the following radical, which needs to be simplified. The book does NO help in explaining how to go about it. ^3sqrt -27y^18/81x^6 After scouring the inte      Log On


   

Question 1125364: Looking for help with the following radical, which needs to be simplified. The book does NO help in explaining how to go about it.
^3sqrt -27y^18/81x^6
After scouring the internet I used quotient rules and broke it down as follows:
^3sqrt-27y^18 / ^3sqrt81x^6
This gave me a result of:
3y^6/3sqrt3^4x^2
Am I on the right track? Thank you!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What you are given is not clear. Maybe you are asking for the cube root of something,...

root%283%2C%28%28-27y%5E18%29%2F%2881x%5E6%29%29%29



You may simplify what is inside first:


root%283%2C%28%28-1%2Ay%5E6%2Ay%5E6%2Ay%5E6%29%2F%283%2A%28x%5E2%29%5E3%29%29%29

You need to understand root%283%2CC%5E3%29=C and also %28root%283%2CC%29%29%5E3=C.

Continuing....
%28%28y%5E6%29%2F%28x%5E2%29%29root%283%2C-1%2F3%29
and you can rationalize the denominator if you want to or need to.

-%28y%5E6%2Fx%5E2%29root%283%2C1%2F3%29

-%28y%5E6%2Fx%5E2%29root%283%2C1%2F3%29root%283%2C3%2F3%29root%283%2C3%2F3%29

-%281%2F3%29%28y%5E6%2Fx%5E2%29%28root%283%2C3%29%29%5E2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Looking for help with the following radical, which needs to be simplified. The book does NO help in explaining how to go about it.
^3sqrt -27y^18/81x^6
After scouring the internet I used quotient rules and broke it down as follows:
^3sqrt-27y^18 / ^3sqrt81x^6
This gave me a result of:
3y^6/3sqrt3^4x^2
Am I on the right track? Thank you!
This is what you came up with: 3y%5E6%2F3sqrt%283%5E4x%5E2%29, I believe.

If this is so, then I must say that you're NOT on the right track. Hopefully, the simplification below will steer you onto the right path.

root%283%2C+%28-+27y%5E18%29%2F%2881x%5E6%29%29 ========> root%283%2C+%28%28-+3%29%5E3%28y%5E6%29%5E3%29%2F3%283%29%5E3%28x%5E2%29%5E3%29%29 ======> root%283%2C+%28-+1%283%29%5E3%28y%5E6%29%5E3%29%2F3%283%29%5E3%28x%5E2%29%5E3%29%29 =======>  =======> highlight%28highlight_green%28highlight%28%28y%5E6%2Fx%5E2%29root%283%2C+-+1%2F3%29%29%29%29

OR, RATIONALIZING the DENOMINATOR in the RADICAND, we get:

%28y%5E6%2Fx%5E2%29root%283%2C+-+1%2F3%29 ===> %28y%5E6%2Fx%5E2%29%28root%283%2C+-+1%29%2Froot%283%2C+3%29%29 ===> %28y%5E6%2Fx%5E2%29%28%28-+1%29%2Froot%283%2C+3%29%29 ===>  =======>  ===> %28y%5E6%2Fx%5E2%29+%2A+%28%28-+1%28root%283%2C+3%29%29%5E2%29%2F3%29 ===> , or