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.
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I think you're right:

{{{root(3,-60)/root(3,120)}}} =

{{{root(3, (-60)/120) }}} =

{{{root(3,-1/2)}}}

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(3,(-1*2*2)/(2*2*2))}}}

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(3,(-1*4)/2^3)}}}

Take cube roots of top and bottom

{{{root(3,-1*4)/root(3,2^3)}}}

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

{{{(root(3, -1)root(3,4))/2}}}

The cube root of -1 is just -1

{{{(-1*root(3,4))/2}}} 

or just

{{{-root(3,4)/2}}}

Yes, you're right.

Edwin</pre>