If a fraction has a surd in the denominator, you can rewrite it such that the denominator is a rational number. This is known as rationalising the denominator.

This can be done by using the following results:

• $(\sqrt{x})^2=x$
• $(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})=x-y$

Rules for rationalising the denominator:

• For fractions of the form $\dfrac{n}{\sqrt{a}}$, multiply by $\dfrac{\sqrt{a}}{\sqrt{a}}$.
• For fractions of the form $\dfrac{n}{a±\sqrt{b}}$, multiply by $\dfrac{a∓\sqrt{b}}{a∓\sqrt{b}}$.