4MA1/2HR Jun 2025, 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 4/(3√5 + 7) and show step by step that it equals a − √b with integers a and b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply top and bottom by 3√5 − 7
- 2Numerator: 4(3√5 − 7) = 12√5 − 28
- 3Denominator: (3√5)² − 7² = 45 − 49 = −4
- 4(12√5 − 28)/(−4) = 7 − 3√5
- 53√5 = √(9 × 5) = √45
- 6= 7 − √45, so a = 7, b = 45
Answer7 − √45
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