Multiplying and Dividing Surds

This page focuses on multiplying and dividing surds in GCSE maths. It explains the rules for these operations and provides examples to illustrate the concepts.

When multiplying surds, multiply the numbers inside the roots and the numbers in front of the roots separately. For example:

Example: √3 × √14 = √(3 × 14) = √42 = √(2 × 21) = √2 × √21 = √2 × 3√7

The page also covers multiplication of surds involving brackets, such as 3(√5 + √3) = 3√5 + 3√3.

For dividing surds, divide the numbers inside the roots and the numbers in front of the roots separately. For instance:

Example: √12 ÷ √3 = √(12 ÷ 3) = √4 = 2

The page includes more complex examples and practice questions, which are crucial for understanding these concepts fully. Students can find additional multiplying and dividing surds worksheets with answers online for extra practice.

Highlight: When multiplying or dividing surds, always simplify the result if possible.

Rationalising the Denominator

This page explains the concept of rationalising the denominator in GCSE maths. It's an important technique for expressing fractions without surds in the denominator.

Definition: Rationalising the denominator is the process of eliminating surds from the denominator of a fraction.

The page provides step-by-step instructions for rationalising denominators with single terms and two terms. For a single term denominator:

1. Multiply both numerator and denominator by the surd in the denominator.
2. Simplify the resulting expression.

Example: Rationalise the denominator of 1/√3 Solution: (1/√3) × (√3/√3) = √3/3

For denominators with two terms (a + b√c), multiply by the conjugate (a - b√c):

Example: Rationalise the denominator of 1/(2 + √3) Solution: (1/(2 + √3)) × ((2 - √3)/(2 - √3)) = (2 - √3)/(4 - 3) = 2 - √3

The page includes practice questions and examples of rationalising surds questions and answers. Students can find more resources like rationalising the denominator corbettmaths for additional practice.

Highlight: Rationalising the denominator is crucial for simplifying expressions and solving equations involving surds.