4MA1/2H Nov 2021, Question 17: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Rationalise 8 divided by (√5 − 1) and write it as √a + b with integers a and b, showing all working stages.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply the numerator and denominator by √5 + 1
- 28/(√5 − 1) = 8(√5 + 1)/((√5 − 1)(√5 + 1))
- 3(√5 − 1)(√5 + 1) = 5 − 1 = 4
- 4= (8√5 + 8)/4
- 5= 2√5 + 2
- 62√5 = √(4 × 5) = √20
- 7So 8/(√5 − 1) = √20 + 2, with a = 20 and b = 2
Answer√20 + 2
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