4MA1/1H Jun 2022, Question 16: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
Without a calculator, show that 12 divided by (√2 − 1) minus (√2)⁵ equals 2√32 + 12, with clear working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply top and bottom by √2 + 1: the bottom (√2 − 1)(√2 + 1) = 1
- 2So 12/(√2 − 1) = 12√2 + 12
- 3(√2)⁵ = (√2)⁴ × √2 = 4√2
- 412√2 + 12 − 4√2 = 8√2 + 12, and 2√32 = 2 × 4√2 = 8√2
- 512 + 8√2
Answer12 + 8√2
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