4MA1/2H Jun 2019, Question 16: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Rationalise the denominator of (4 + √8)/(√2 − 1) to express it as a + b√2 with integers a and b, showing all working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1(4 + √8) ÷ (√2 − 1)
- 2Multiply numerator and denominator by (√2 + 1)
- 3Numerator: (4 + √8)(√2 + 1) = 4√2 + 4 + √8 × √2 + √8
- 4√8 × √2 = √16 = 4 and √8 = 2√2
- 5Numerator = 4√2 + 4 + 4 + 2√2 = 8 + 6√2
- 6Denominator: (√2 − 1)(√2 + 1) = 2 − 1 = 1
- 7So (4 + √8) ÷ (√2 − 1) = 8 + 6√2
- 8a = 8 and b = 6
Answera = 8 and b = 6
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