4024/11 Oct/Nov 2025, Question 23: Surds
Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Simplify √8 × √6 + √3, and rationalise the denominator of 3/(2 − √5), simplifying the result.
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Part (a) · 2 marks
Simplify √8 × √6 + √3.
- 1√8 × √6 = √48 = √16 × √3 = 4√3
- 24√3 + √3 = 5√3
Answer5√3
Part (b) · 3 marks
Rationalise the denominator of 3/(2 − √5) and simplify.
- 13/(2 − √5) × (2 + √5)/(2 + √5)
- 2Denominator: (2 − √5)(2 + √5) = 4 + 2√5 − 2√5 − 5 = −1
- 3= 3(2 + √5)/(−1) = −6 − 3√5
Answer−3(2 + √5) or −(6 + 3√5) or −6 − 3√5
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Also searched as: 4024/11/O/N/25 · 4024_w25_qp_11 · 4024 w25 11 · question 23.
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