4MA1/1HR Jan 2019, Question 18: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
Show that √8/(√8 − 2) can be written as n + √n for an integer n, showing working clearly.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply the top and the bottom of √8/(√8 − 2) by √8 + 2
- 2Top: √8(√8 + 2) = 8 + 2√8
- 32√8 = 2 × 2√2 = 4√2, so the top is 8 + 4√2
- 4Bottom: (√8 − 2)(√8 + 2) = 8 − 4 = 4
- 5So √8/(√8 − 2) = (8 + 4√2) ÷ 4
- 6(8 + 4√2) ÷ 4 = 8/4 + 4√2/4 = 2 + √2
- 72 + √2 is of the form n + √n with n = 2, so √8/(√8 − 2) = 2 + √2
Answer2 + √2
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