4MA1/2HR Jun 2023, Question 16: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
Rationalise 2√3/(√3 − 1) and show it equals a + √a for integer a, with clear working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 12√3 / (√3 − 1) × (√3 + 1) / (√3 + 1)
- 2(2√3(√3 + 1)) / ((√3 − 1)(√3 + 1))
- 3(2×3 + 2√3) / (3 − 1)
- 4(6 + 2√3) / 2
- 56/2 + (2√3)/2
- 63 + √3
- 7√3 + 3
Answer3 + √3
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