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\(\sqrt{[200\sqrt{[200\sqrt{[200....... \infty ]}]}]} = ?\)

  • A.200
  • B.10
  • C.1
  • D.20

Answer: A

Exp: Let \(\sqrt{[200\sqrt{[200\sqrt{[200....... \infty ]}]}]} = x\).

Hence \(\sqrt{200x} = x\)

Squaring both sides \(200x = x^2\)

\(\Rightarrow x(x-200) = 0\)

\(\Rightarrow x = 0 \) or \(x-200 = 0\) i.e. \(x = 200\)

As \(x\) cannot be 0, \(x = 200\)

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