- A-Level Maths

# Indices & Algebraic Methods

When working with indices, there are eight laws that must be followed:

These can be used to factorise and expand expressions.

### Surds

Surds are examples of irrational numbers, meaning they do not follow a repeating pattern but go on forever, uniquely. Pi is the most common example of an irrational number, but surds are slightly different - they are **the square roots of non-square numbers**.

√4 = 24 is a square number, so gives a rational square root

√2 = 1.4142...2 is not a square number, so its square root is irrational

Like with indices, there are rules that apply to surds:

These can be used to **rationalise denominators:**

For fractions in the form

**1 / √a**, multiply both numerator and denominator by**√a**For fractions in the form

**1 / (a + √b)**, multiply both numerator and denominator by**(a - √b)**For fractions in the from

**1 / (a - √b)**, multiply both numerator and denominator by**(a + √b)**

This is known as the conjugate pair (switching the sign of the denominator)

## Algebraic Fractions

To simplify algebraic fractions, factorise whatever can be factorised so that parts of the numerator and denominator can cancel:

### Multiplication

To multiply fractions, any common factors can be cancelled before multiplying the numerators and denominators.