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OAU Post-UTME Mathematics 2011 Question 16

Question 16

Surds

Find the value of √(6 + √(6 + √(6 + √(6 + …))))

  1. A.−2
  2. B.2
  3. C.6
  4. D.3
Show the answer and explanation

Answer: D (3)

Explanation

Let x be the value. Then x² = 6 + x, so x² − x − 6 = 0 and x = 3 or −2. A square root can't be negative, so x = 3.