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4MA1/1HR Jun 2024, Question 17: Surds

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Find n from (fourth root of k to the 12) to the 5 equals k to the n, and write 7/(2 − √3) as √c + d with integers c and d.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Find the value of n in (∜(k¹²))⁵ = kⁿ.

  1. 1⁴√(k¹²) = k^(12/4) = k³
  2. 2(k³)⁵ = k^(3 × 5) = k¹⁵
  3. 3So n = 15

Answer15

Part (b) · 3 marks

Express 7/(2 − √3) in the form √c + d, integers c and d, showing working.

  1. 1Multiply the top and the bottom by 2 + √3
  2. 2Bottom: (2 − √3)(2 + √3) = 4 − 3 = 1
  3. 3Top: 7(2 + √3) = 14 + 7√3, so the fraction is 14 + 7√3
  4. 4The form asked for is √c + d, so write 7√3 as one root: 7√3 = √(49 × 3) = √147
  5. 5So the answer is √147 + 14

Answer√147 + 14

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