0580/21 Oct/Nov 2025, Question 21: Surds
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks
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The question, in short
Expand a product of surds to find integers a and b, then rationalise 6/√2 into simplest form.
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Part (a) · 2 marks
Expand (3 − √5)(2 + 3√5) and find the values of a and b where it equals a + b√5.
- 1(3 − √5)(2 + 3√5) = 6 + 9√5 − 2√5 − 3 × 5
- 2= 6 − 15 + 7√5 = −9 + 7√5
- 3a = −9, b = 7
Answera = −9, b = 7
Part (b) · 2 marks
Rationalise the denominator of 6/√2 and give the answer in simplest form.
- 16/√2 × √2/√2 = 6√2/2
- 2= 3√2
Answer3√2
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Also searched as: 0580/21/O/N/25 · 0580_w25_qp_21 · 0580 w25 21 · question 21.
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