0580/23 May/Jun 2026, Question 21: Surds
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks
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The question, in short
Simplify the square of √0.1, then rationalise the denominator of 4/(2 − √2) and give the result in simplest form.
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Part (a) · 1 mark
Simplify the expression (√0.1)².
- 1(√0.1)² = 0.1
Answer0.1
Part (b) · 3 marks
Rationalise the denominator of 4/(2 − √2), giving the answer in its simplest form.
- 1Multiply by (2 + √2)/(2 + √2)
- 2Numerator: 4(2 + √2) = 8 + 4√2
- 3Denominator: 4 + 2√2 − 2√2 − 2 = 2
- 4(8 + 4√2)/2 = 4 + 2√2
Answer4 + 2√2
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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 21.
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