Question

Find the value of sqrt (6 sqrt(6 sqrt (6 sqrt(...))))

Answer 1

Answer:

Refer to the attachment!!

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Answer 2

$let \: \: x = \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{..} } } } \\ \: \: \: \: \: {x}^{2} = 6 \sqrt{6 \sqrt{6 \sqrt{6...} } } \\ \: \: \: \: \: \frac{ {x}^{2} }{6} = \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{6..} } } } \\ \: \: \: \: \: \frac{ {x}^{2} }{6} = x \\ \: \: \: \: \: {x}^{2} = 6x \\ \: \: \: x = 6$

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