Just been trying to think of an example of rationalising and the only thing I could think of is rationalising the denominator or a fraction containing a surd.

As you may or may not know, a surd is a number such as

that cannot be express as a 'normal' number, ie. you can't write it as a finite decimal.

Fractions containing surds as a denominator aren't considered to be 'elegent' as my maths tutor once put it. For example:

can be rationalised to become

by multiplying by

, this is considered rationalised.

Another example is where you have a fraction such as

.

To deal with this you use the

Difference of two squares identity, multiplying top and bottom by

.

This gives you

Hope it was something like this that you were looking for, if there is anything more that you don't understand please post back