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JAMB Mathematics 1981 Question 19

Question 19

Surds

Simplify √2/(√3 − √2) − (√3 − √2)/(√3 + √2)

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

Answer: B (3(√6 − 1))

Explanation

√2/(√3 − √2) = √2(√3 + √2) = √6 + 2, and (√3 − √2)/(√3 + √2) = (√3 − √2)² = 5 − 2√6. The difference is 3√6 − 3 = 3(√6 − 1).