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0580/21 May/Jun 2026, Question 26: Surds

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 7 marks

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The question, in short

Two surd questions: expand and simplify a product of brackets, then find the constant k in an equation involving a mixed-number square root and a fraction.

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

Part (a) · 3 marks

Expand and simplify (5 + √2)(3 − √8), giving the result in simplest surd form.

  1. 1(5 + √2)(3 − √8) = 15 − 5√8 + 3√2 − √16
  2. 2= 15 − 10√2 + 3√2 − 4
  3. 3= 11 − 7√2

Answer11 − 7√2

Part (b) · 4 marks

Given √(2 9/20) + 6/√5 = k√5, find the value of k.

  1. 1√(2 9/20) = √(49/20) = 7/√20 = 7/(2√5)
  2. 26/√5 = 12/(2√5)
  3. 3Sum = 19/(2√5) = 19√5/10
  4. 4k = 19/10 = 1.9

Answer1.9

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Also searched as: 0580/21/M/J/26 · 0580_s26_qp_21 · 0580 s26 21 · question 26.
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