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0580/22 Feb/Mar 2025, Question 20: Surds

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 5 marks

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The question, in short

Simplify a sum of two square roots, then rationalise a fraction with a surd denominator and simplify it.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Simplify √300 + √48.

  1. 1√300 = √100 × √3 = 10√3
  2. 2√48 = √16 × √3 = 4√3
  3. 310√3 + 4√3 = 14√3

Answer14√3

Part (b) · 3 marks

Rationalise the denominator of 9/(2 + √7) and simplify the result.

  1. 1Multiply top and bottom by (2 − √7)
  2. 29(2 − √7)/((2 + √7)(2 − √7)) = 9(2 − √7)/(4 − 7)
  3. 3= 9(2 − √7)/(−3) = −3(2 − √7)
  4. 4= 3(√7 − 2)

Answer3(√7 − 2)

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Also searched as: 0580/22/F/M/25 · 0580_m25_qp_22 · 0580 m25 22 · question 20.
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