rationalize this expression (in the description)

Question

I tried changing the surd in the denominator into a fractional indices but I have no idea what to do after that

Answer 1

Hint

If the root in the denominator were a square root you would use the difference of two squares identity to rationalise it.

There is an identity for the difference of two cubes as well: $a^3-b^3=(a-b)(a^2+ab+b^2)$

So, let $(a-b)=\sqrt[3]{2}-1$.

This suggests that you multiply your expression by $\frac {(a^2+ab+b^2)}{(a^2+ab+b^2)}$.