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: $3\sqrt{3}$
Answer (1)
24th Jan, 2024
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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