Rationalise the denominator means eliminating the SURD from the denominator. Here are a few examples showing how to do this operation. A full video lesson on working with SURDS is provided here.

Rationalise 1/√2

Rationalise 2/5√3

Rationalise (2√8) / (5√2 )

Rationalise (2) / (5-√3 )

and finally…. an exam type question

Circle Theorems (IV - VII)
Trig Ratios - Must Know Values