SOLUTION: I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain.

Algebra ->  Radicals -> SOLUTION: I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain.      Log On


   

Question 78945: I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain.

I think you're right:

root%283%2C-60%29%2Froot%283%2C120%29 =

root%283%2C+%28-60%29%2F120%29+ =

root%283%2C-1%2F2%29

Rationalize the denominator.

The denominator needs 2 more factors
of 2 to become a perfect cube, so
we multiply the fraction under the
radical by 2*2.  But if you
multiply the denominator by 2*2
you must multiply the numerator by
2*2 also.

root%283%2C%28-1%2A2%2A2%29%2F%282%2A2%2A2%29%29

The 2*2*2 on the bottom can be
written as 2³, and the 2*2 in the
top can be written as 4

root%283%2C%28-1%2A4%29%2F2%5E3%29

Take cube roots of top and bottom

root%283%2C-1%2A4%29%2Froot%283%2C2%5E3%29

Take individual cube roots of -1 and 4
in the top and taking the cube root of 
the bottom jsut gives 2

%28root%283%2C+-1%29root%283%2C4%29%29%2F2

The cube root of -1 is just -1

%28-1%2Aroot%283%2C4%29%29%2F2 

or just

-root%283%2C4%29%2F2

Yes, you're right.

Edwin