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4024/13 May/Jun 2026, Question 22: 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 fraction with 3 + √7 in the denominator, giving the simplest form.

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

Part (a) · 2 marks

Simplify √98 − √18.

  1. 1√98 = √49 × √2 = 7√2
  2. 2√18 = √9 × √2 = 3√2
  3. 37√2 − 3√2 = 4√2

Answer4√2

Part (b) · 3 marks

Rationalise the denominator of 5/(3 + √7) and give the answer in its simplest form.

  1. 1Multiply by (3 − √7)/(3 − √7)
  2. 2Denominator: (3 + √7)(3 − √7) = 9 − 7 = 2
  3. 3Numerator: 5(3 − √7) = 15 − 5√7
  4. 4= (15 − 5√7)/2

Answer5(3 − √7)/2 or (15 − 5√7)/2

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Also searched as: 4024/13/M/J/26 · 4024_s26_qp_13 · 4024 s26 13 · question 22.
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