• # Revision:Indices and Surds

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Indices and Surds

Indices are used to describe the general term for in say . There are a few laws to know when manipulating expressions involving indices.

## Surds

Surds are basically an expression involving a root, squared or cubed etc...

There are some basic rules when dealing with surds

Also notice the special case

### Difference of Two Squares

This is called the difference of two squares

### Rationalising Surds

When you have a fraction where both the nominator and denominator are surds, rationalising the surd is the process of getting rid of the surd on the denominator.

To rationalise a surd you multiply top and bottom by fraction that equals one. Take the example shown below

To rationalise this multiply by effectively 1

Can you see why was chosen? This is because so the denominator becomes surd free.

For a more complex term

First of all, we need to get rid of the surd expression on the bottom, you should remember the difference of two squares formula.

suppose a = 1 and b =

So to get rid of the denominator surd we multiply by like so.

In general

• Fractions in the form multiply top and bottom by
• Fractions in the form multiply the top and bottom by
• Fractions in the form multiply the top and bottom by
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