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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)(√3√3)`

`= frac(27√3)(3)`

`= 9√3`

Answer: 9√3

Example 2

Rationalise `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`

Answer: 4√2

See also Manipulating Algebraic Fractions and Working with Roots in Algebra