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GATE 2014 CS (CS2) – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Evaluate $\sqrt{12+\sqrt{12+\sqrt{12+\cdots}}}$.

  1. 3.464
  2. 3.932
  3. 4.000
  4. 4.444

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Correct answer: (C) 4.000

Explanation

Let the convergent nonnegative expression be x. Its self-similarity gives x=√(12+x), hence x²−x−12=(x−4)(x+3)=0. Nonnegativity excludes−3, leaving **4.000,C**. Iterated positive radicals converge to this fixed point.