0580/22 May/Jun 2026, Question 17: Surds: expanding and rationalising
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 5 marks
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The question, in short
Expand a product of two surd brackets, then rationalise the denominator of a fraction.
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Part (a) · 2 marks
Expand and simplify (4 − √7)(3 + 2√7).
- 1(4 − √7)(3 + 2√7) = 12 + 8√7 − 3√7 − 2 × 7
- 2= 12 − 14 + 5√7
- 3= −2 + 5√7
Answer−2 + 5√7
Part (b) · 3 marks
Rationalise and simplify 2/(3 − √5).
- 1Multiply by (3 + √5)/(3 + √5)
- 2Numerator: 2(3 + √5) = 6 + 2√5
- 3Denominator: 9 − 5 = 4
- 4(6 + 2√5)/4 = (3 + √5)/2
Answer(3 + √5)/2
Stuck on a step? Read the free lesson: Surds
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Also searched as: 0580/22/M/J/26 · 0580_s26_qp_22 · 0580 s26 22 · question 17.
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