Rationalising the Denominator

This page focuses on the important technique of rationalising the denominator when working with surds. This skill is crucial for National 5 Maths Surds past paper questions.

Definition: Rationalising the denominator means turning the surd at the bottom of a fraction into a whole number, while keeping the fraction the same.

The page explains that it's not possible to add or subtract surds with different surd signs. For example, √5 + √3 cannot be simplified further.

Highlight: Rationalising the denominator is important for various mathematical reasons and is a common requirement in National 5 Maths problems.

The method for rationalising the denominator is clearly explained: Multiply both the numerator and denominator by the surd in the denominator.

Three examples are provided to illustrate this process:

1. Rationalising 1/(3√2)
2. Rationalising √8/√8
3. Rationalising 3√8/4

These examples demonstrate the step-by-step process of rationalising denominators with different types of surds, which is essential practice for National 5 Maths Surds revision worksheets.

Example: To rationalise 1/(3√2), multiply both numerator and denominator by √2: (1 × √2) / (3√2 × √2) = √2 / 6

This page provides valuable practice for students preparing for National 5 Maths exams, where rationalising denominators is a common topic in Surds questions.