The value of sqrt(12 + sqrt(12 + sqrt(12 + ...))) is A. 3.464 B. 3.332 C. 4.000 D. 4.441

GATE 2014 · General Aptitude · Number Series · easy

Answer: 4

1. Set up the self-similar equation: Let L = sqrt(12 + sqrt(12 + sqrt(12 + ...))). Since the expression is infinite, the portion inside the outer root is again L. So L = sqrt(12 + L).
2. Solve the resulting quadratic: Squaring: L^2 = 12 + L. Rearranging: L^2 - L - 12 = 0. Factoring: (L - 4)(L + 3) = 0. So L = 4 or L = -3.