How to Rationalise Surds

Rationalising Surds

A key skill involved with SURDS is the ability to rationalise the denominator of a surd. This allows more complex calculations involving fractions to be undertaken more easily
Rationalising SURDS basically involves finding an equivalent fraction which has the surd in the numerator rather than the denominator

The key fact to use when rationalising simple surds is that:

Squaring surds

So for example:

Squaring root of 5

Simple Examples of Rationalising

When we have simple fractions, to rationalise we merely multiply by the surd contained with the denominator

Written Example 1:

Simple example of rationalising

Written Example 2:

Slightly more complex example of rationalising

Click Below for a VIDEO tutorial on rationalising surds
Link to video

More complex example of Rationalising

When we have a more complex denominator we use the difference of two squares to simplify and hence rationalise the denominator. To do this we multiply by the denominator with the sign changed. See the example below to clarify this:


SURDS and the difference of two squares

Written Example 3:

Rationalising more complex Surds