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JAMB Mathematics 1980 Question 4

Question 4

Surds

Rationalize the denominator of the given expression (√(1 + a) − √a)/(√(1 + a) + √a)

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

Answer: A (1 + 2a − 2√(a(1 + a)))

Explanation

Multiply top and bottom by √(1 + a) − √a. The bottom becomes (1 + a) − a = 1 and the top (√(1 + a) − √a)² = 1 + 2a − 2√(a(1 + a)).