SOLUTION: I need help rationalizing.... 9 times the cubic root 2 over/divided by the cubic root 5 minus cubic root 2. Please help! Soory my keyboard will not allow me to type the equati

Question 203195: I need help rationalizing....
9 times the cubic root 2 over/divided by the cubic root 5 minus cubic root 2.
Please help! Soory my keyboard will not allow me to type the equation.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Let and

Replace each with "x" and each with "y"

Now this is where you have to get a bit creative. It's very helpful to remember that . Why is this important? Because if you cube a cube root, they will both cancel out (leaving the stuff inside as a remainder).

So if we multiply both numerator and denominator by , we get:

Use the identity given above

Plug in and

Cube the cube roots (to eliminate them)

Subtract

Reduce

Combine the roots.

Multiply

Use the identity

Square 5 to get 25 and square 2 to get 4

Distribute

Combine the roots.

Multiply

==================================================================

Answer:

So

This can be verified (as I have verified it myself) with a calculator.
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