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0580/23 May/Jun 2025, Question 15: Surds

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 6 marks

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The question, in short

Simplify surd expressions: add two square roots, find integer k in a quotient of surds, and rationalise a denominator with a surd.

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

Part (a) · 2 marks

Simplify √27 + √12, giving the answer in simplest surd form.

  1. 1√27 = √9 × √3 = 3√3; √12 = √4 × √3 = 2√3
  2. 23√3 + 2√3 = 5√3

Answer5√3

Part (b) · 2 marks

Given 40√8 divided by 5√2 equals k, where k is an integer, find k.

  1. 1√8 = 2√2
  2. 2(40 × 2√2)/(5√2) = 80/5
  3. 3k = 16

Answer16

Part (c) · 2 marks

Rationalise the denominator of 1/(3 − √5).

  1. 11/(3 − √5) × (3 + √5)/(3 + √5)
  2. 2= (3 + √5)/(9 − 5)
  3. 3= (3 + √5)/4

Answer(3 + √5)/4

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 15.
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