Page 2: Adding and Subtracting Surds

The page explains the rules for combining like surds through addition and subtraction operations.

Highlight: Only surds with the same number inside the root can be added or subtracted.

Example: √80 + √125 can be simplified to 4√5 + 5√5 = 9√5

Definition: Like surds are surds that have the same number under the root sign.

Vocabulary: Terms - the parts of an expression separated by + or - signs.

Page 3: Multiplying Surds

This section covers the multiplication of surds and how to simplify the results.

Definition: When multiplying surds, multiply the numbers outside the root signs together and the numbers inside the root signs together.

Example: 3√2 × 5√12 = 15√24 = 30√6

Highlight: Always simplify the final answer if possible by finding square factors.

Page 4: Worded Problems with Surds

The page demonstrates how to apply surd operations to solve real-world problems, particularly focusing on area calculations.

Example: Finding the area of a triangle using surds: Area = ½ × base × height

Highlight: When expanding brackets containing surds, multiply each term carefully.

Page 5: Dividing Surds

This section explains the process of dividing surds and rationalising denominators.

Definition: To divide surds, divide the numbers outside the root signs and divide the numbers inside the root signs separately.

Highlight: When dividing surds with two terms in the denominator, multiply both numerator and denominator by the conjugate of the denominator.

Example: 16√24 ÷ 8 = 2√3

Page 6: Rationalising the Denominator

The final page focuses on the technique of rationalising denominators to eliminate surds from the bottom of fractions.

Definition: Rationalising the denominator means eliminating any surds from the denominator of a fraction.

Highlight: To rationalise a single surd denominator, multiply both numerator and denominator by the same surd.

Example: √3/√2 becomes (√3 × √2)/(√2 × √2) = √6/2

Page 1: Simplifying Surds

This page introduces the fundamental concepts of simplifying surds through multiple examples. Students learn to break down numbers under square roots into their simplest form.

Definition: A surd is an expression that contains an irrational root, typically a square root that cannot be simplified to a whole number.

Highlight: Square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) are essential for simplifying surds.

Example: √8 can be simplified to 2√2 by identifying the largest square factor (4) and writing √8 as √4 × √2.