0580/22 May/Jun 2025, Question 18: Surds
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks
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The question, in short
Rationalise a surd fraction and expand a product of two surd brackets, giving the integer and surd coefficients.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Rationalise the denominator of 9/√3 and simplify fully.
- 19/√3 × √3/√3 = 9√3/3
- 2= 3√3
Answer3√3
Part (b) · 2 marks
Expand (5 − √2)(1 + 3√2) and find the values of c and k in c + k√2.
- 1(5 − √2)(1 + 3√2) = 5 + 15√2 − √2 − 3 × 2
- 2= −1 + 14√2
- 3c = −1, k = 14
Answerc = −1, k = 14
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Also searched as: 0580/22/M/J/25 · 0580_s25_qp_22 · 0580 s25 22 · question 18.
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