In this deck, we'll explore how to rationalise the denominator of a fraction. This is a standard technique in algebra for rewriting fractions that have a surd, like the square root of 2, in the denominator.

First, let's quickly recap what we mean by rational and irrational numbers. A rational number can be written as a simple fraction, like one half or the number 5. An irrational number cannot, and its decimal representation goes on forever without repeating. Surds are a common type of irrational number.

So why do we 'rationalise' the denominator? It's a bit like simplifying fractions. It's a mathematical convention to write expressions in a standard form, which makes them easier to work with, compare, and use in further calculations.

Let's start with the first type, where the denominator is a single surd term. For example, the fraction '1 over the square root of 5'.