Worked Example 5: Expanding with Surds
Part of Surds · GCSE GCSE Mathematics revision
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 15 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 15
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.
Practice Questions for Surds
Which of these is the simplified form of √48?
Explain why it is preferable to write fractions in rationalized form rather than leaving a surd in the denominator.
Quick Recall Flashcards
14 questions on Surds — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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