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