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JAMB Mathematics 1997 Question 7

Question 7

Surds

Simplify (2√3 + 3√5)/(3√5 − 2√3)

  1. A.(19 + 4√15)/11
  2. B.(19 + 4√15)/19
  3. C.(19 + 2√15)/11
  4. D.(19 + 2√15)/19
Show the answer and explanation

Answer: A ((19 + 4√15)/11)

Explanation

Multiply top and bottom by (3√5 + 2√3). The top becomes (2√3 + 3√5)² = 57 + 12√15 and the bottom 45 − 12 = 33. Dividing by 3 gives (19 + 4√15)/11.