## Main problem

Can you rationalise the denominator of the following fractions?

To rationalise the denominator, we need to multiply by something which gives us an integer as an answer.

How do we do this when there are square roots in the denominator? How could we adapt that method (or those methods) to help us here?

1. $\dfrac{1}{1+\sqrt[3]{2}}$

(If you need some suggestions on how to get started, have a look at the Suggestion section.)

2. $\dfrac{1}{2+\sqrt[3]{2}}$

3. $\dfrac{1}{\sqrt[3]{2} + \sqrt[3]{4}}$

4. $\dfrac{1}{1 - \sqrt[3]{2} + \sqrt[3]{4}}$