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WAEC Further Mathematics 2020 Question 7

Question 7

Surds

Simplify: (√5 + 3)/(4 − √10)

  1. A.⅔√5 + ⅚√2 + 2
  2. B.⅔√5 + ⅚√2 + ½√10
  3. C.⅔√5 + ⅚√2 + ½√10 + 2
  4. D.⅔√5 − ⅚√2 − ½√10 + 2
Show the answer and explanation

Answer: C (⅔√5 + ⅚√2 + ½√10 + 2)

Explanation

Multiply by (4 + √10)/(4 + √10): (4√5 + √50 + 12 + 3√10)/6 = (4√5 + 5√2 + 12 + 3√10)/6 = ⅔√5 + ⅚√2 + ½√10 + 2.