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0580/23 Oct/Nov 2025, Question 24: Surds

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

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The question, in short

Simplify surd expressions, find the area constant k of a rectangle with sides 3√8 cm and 2√2 cm, and rationalise a denominator.

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

Part (a) · 2 marks

Simplify √125 − √20.

  1. 1√125 = √(25 × 5) = 5√5 and √20 = √(4 × 5) = 2√5
  2. 25√5 − 2√5 = 3√5

Answer3√5

Part (b) · 2 marks

Rectangle has sides 3√8 cm and 2√2 cm; its area is k cm². Work out k.

  1. 1k = 3√8 × 2√2 = 6√16
  2. 2= 6 × 4 = 24

Answer24

Part (c) · 2 marks

Rationalise the denominator of 1/(√7 + 2).

  1. 11/(√7 + 2) × (√7 − 2)/(√7 − 2)
  2. 2= (√7 − 2)/(7 − 4) = (√7 − 2)/3

Answer(√7 − 2)/3 or (1/3)√7 − 2/3

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Also searched as: 0580/23/O/N/25 · 0580_w25_qp_23 · 0580 w25 23 · question 24.
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