Surd Denominators

## Surd Denominators

When a surd forms part of a denominator in a fraction, it must be removed.

The surd can be removed by multiplying both the numerator and the denominator by the value of the surd. For example, multiply frac(√a)(√b) by frac(√b)(√b), and simplify to frac(a√b)(b).

This process is called rationalising the denominator, as the denominator becomes a rational number.

## Example 1

Rationalise and simplify: frac(27)(√3)

frac(27)(√3)

= frac(27√3)(√3√3)

= frac(27√3)(3)

= 9√3

## Example 2

Rationalise frac(8√3)(√6).

frac(8√3)(√6)

= frac(8√3)(√2√3)

= frac(8)(√2)

= frac(8)(√2) xx frac(√2)(√2)

= frac(8√2)(√2√2)

= frac(8√2)(2)

= 4√2