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WAEC Further Mathematics 2016 Question 2

Question 2

Surds

Express (8 − 3√6)/(2√3 + 3√2) in the form p√3 + q√2

  1. A.7√3 − (17/3)√2
  2. B.−(17/3)√3 + 7√2
  3. C.(17/3)√3 − 7√2
  4. D.−7√3 − (17/3)√2
Show the answer and explanation

Answer: B (−(17/3)√3 + 7√2)

Explanation

Multiply by (2√3 − 3√2)/(2√3 − 3√2): numerator 16√3 − 24√2 − 18√2 + 18√3 = 34√3 − 42√2; denominator 12 − 18 = −6. Result −(17/3)√3 + 7√2.