Question : The value of $\sqrt{3\sqrt{3\sqrt{3......}}}$ is equal to:
Option 1: $\sqrt{3}$
Option 2: $3$
Option 3: $2\sqrt{3}$
Option 4: $3\sqrt{3}$
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Correct Answer: $3$
Solution : Given: $\sqrt{3\sqrt{3\sqrt{3......}}}$ Let $x = \sqrt{3\sqrt{3\sqrt{3......}}}$ $ ⇒ x = \sqrt{3x}$ By squaring both sides, we get: $ ⇒ x^{2} = 3x$ $ ⇒ x = 3$ Hence, the correct answer is $3$.
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