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WAEC Further Mathematics 2015 Question 1

Question 1

Surds

Simplify: (1 − 2√5)/(2 + 3√2)

  1. A.14(2√2 + 6√5 − 4√10)
  2. B.(1/14)(2 − 3√2 − 4√5 − 6√10)
  3. C.(1/14)(3√2 + 4√5 − 6√10 − 2)
  4. D.14(2 + 3√2 − 6√5 + 4√10)
Show the answer and explanation

Answer: C ((1/14)(3√2 + 4√5 − 6√10 − 2))

Explanation

Multiply top and bottom by (2 − 3√2): numerator 2 − 3√2 − 4√5 + 6√10, denominator 4 − 18 = −14. Dividing by −14 gives (1/14)(3√2 + 4√5 − 6√10 − 2).