0580/21 May/Jun 2025, Question 15: Surds
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks
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The question, in short
Expand and simplify a product of two surd brackets, then rationalise a fraction with a surd denominator, giving the simplest form.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Expand and simplify (2 − √5)(1 − 3√5).
- 1(2 − √5)(1 − 3√5) = 2 − 6√5 − √5 + 3 × 5
- 2= 2 − 7√5 + 15
- 3= 17 − 7√5
Answer17 − 7√5
Part (b) · 2 marks
Rationalise the denominator of 6/√10 and give the answer in simplest form.
- 16/√10 × √10/√10 = 6√10/10
- 2= (3√10)/5
Answer(3√10)/5
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Also searched as: 0580/21/M/J/25 · 0580_s25_qp_21 · 0580 s25 21 · question 15.
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