NumberStudy Notes

Worked Example 5: Expanding with Surds

Part of Surds — GCSE Mathematics

This study notes covers Worked Example 5: Expanding with Surds within Surds for GCSE Mathematics. Revise Surds in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 11 of 14 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 11 of 14

Practice

14 questions

Recall

22 flashcards

Worked Example 5: Expanding with Surds

Expand: (2 + √5)(3 - √5)

Solution

Use FOIL method:

= 2×3 + 2×(-√5) + √5×3 + √5×(-√5)

= 6 - 2√5 + 3√5 - 5

= 1 + √5

Answer: 1 + √5

Keep building this topic

Read this section alongside the surrounding pages in Surds. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 4: Rationalizing Higher Level: Complex Rationalization The Exact Truth What Are Surds?

Practice Questions for Surds

Which of these is the simplified form of √48?

A. 12√2
B. 4√3
C. 3√4
D. 6√2

1 markfoundation

Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.

2 markshigher

Quick Recall Flashcards

What is a surd?

An irrational root that cannot be simplified to a whole number Examples: √2, √3, √5, ∛7 NOT surds: √4 = 2, √9 = 3 (these simplify to whole numbers)

What are Like Surds?

Surds with the same root part Examples of like surds: • 3√2 and 5√2 (both have √2) • 2√7 and -4√7 (both have √7) Can add/subtract like surds: 3√2 + 5√2 = 8√2

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Worked Example 4: Rationalizing

Higher Level: Complex Rationalization