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.
Rationalise and simplify: `frac(27)(√3)`
`frac(27)(√3)`
`= frac(27√3)(√3√3)`
`= frac(27√3)(3)`
`= 9√3`
Answer: 9√3
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`
Answer: 4√2