Surds are numbers left in square root form that are used when detailed accuracy is required in a calculation. They are numbers which, when written in decimal form, would go on forever.
A fraction with a surd in the denominator can be simplified so that the denominator is an integer. This is called rationaliseTo remove the square root from a denominator. the denominator.
Example
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 \(\sqrt{6}\).