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4024/13 May/Jun 2025, Question 25: Surds

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Simplify a difference of two square roots, then rationalise a denominator and give the result in simplest form.

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

Part (a) · 2 marks

Simplify √300 − √48.

  1. 1√300 = √(100 × 3) = 10√3
  2. 2√48 = √(16 × 3) = 4√3
  3. 310√3 − 4√3 = 6√3

Answer6√3

Part (b) · 3 marks

Rationalise the denominator of 6/(√7 + 2) and give the simplest form.

  1. 16/(√7 + 2) × (√7 − 2)/(√7 − 2)
  2. 2Denominator: (√7 + 2)(√7 − 2) = 7 − 4 = 3
  3. 3= 6(√7 − 2)/3
  4. 4= 2(√7 − 2) = 2√7 − 4

Answer2(√7 − 2) or 2√7 − 4

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Also searched as: 4024/13/M/J/25 · 4024_s25_qp_13 · 4024 s25 13 · question 25.
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