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4024/12 May/Jun 2022, Question 13: Further Powers and Roots

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Evaluate an expression involving square and cube roots, then give an irrational number n within the interval 4.5 to 5.5.

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

Part (a) · 2 marks

Evaluate (√9 × ∛64)².

  1. 1√9 = 3 and ∛64 = 4
  2. 2(3 × 4)² = 12²
  3. 3= 144

Answer144

Part (b) · 1 mark

Write down an irrational value of n satisfying 4.5 ≤ n ≤ 5.5.

  1. 14.5² = 20.25 and 5.5² = 30.25, so √n works for 20.25 ≤ n ≤ 30.25
  2. 2√21 is irrational and √21 ≈ 4.58, which is in the range
  3. 3n = √21

AnswerIrrational number in range 4.5 ≤ n ≤ 5.5

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Also searched as: 4024/12/M/J/22 · 4024_s22_qp_12 · 4024 s22 12 · question 13.
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