Quote:

Rationalize the denominator: .$\displaystyle \frac{1\,-\,\sqrt{2}}{2\sqrt{3}\,-\,\sqrt{6}}$

So I multilply by the conjugate & simplify: $\displaystyle \frac{\sqrt{6}\,-\,2\sqrt{6}}{12\,-\,6}\;=\boxed{\;-\,\frac{\,\sqrt{6}}{6}}$ . . . . Right!

Now this beastly problem w/the same directions: $\displaystyle \sqrt[3]{\frac{16}{9}}$

I thought to write it like this: $\displaystyle \frac{\sqrt[3]{16}}{\sqrt[3]{9}}$

Then multiply the top and bottom by $\displaystyle \sqrt[3]{3}$: $\displaystyle \frac{\sqrt[3]{48}}{3}\,=\,\boxed{\frac{2\sqrt[3]{6}}{3}}$ . . . . Great!