Rationalising denominators - Higher - Surds - AQA - GCSE Maths Revision - AQA

Rationalising denominators - Higher

A fraction with a surd in the denominator can be simplified so that the denominator is an integer. This is called the denominator.

Simplify \(\frac{\sqrt{8}}{\sqrt{6}}\)

First simplify \(\sqrt{8}\).

\(\sqrt{8} = \sqrt{4 \times 2}\)

\(= \sqrt{4} \times \sqrt{2}\)

\(= 2\sqrt{2}\)

Then multiply the numerator and denominator by \(\sqrt{6}\).

\(\frac{2\sqrt{2} \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}}\)

\(= \frac{2\sqrt{12}}{6}\)

\(= \frac{4\sqrt{3}}{6} = \frac{2\sqrt{3}}{3}\)

Rationalise the denominator of the following: