Question

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$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} } } } }$
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Answer 1

$\huge\mathfrak\red{Answer}$

$let \: \\ x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 } } } } \\ \\ squaring \: on \: both \: side \\ \\ {x}^{2} = 6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} } } } \\ \\ we \: let \: above \: x = \sqrt{6 + \sqrt{6 + \sqrt{6} } } \\ \\ {x}^{2} = 6 + x \\ {x}^{2} - x - 6 = 0 \\ {x}^{2} - 3x + 2x - 6 = 0 \\ x(x - 3) + 2(x - 3) = 0 \\ (x + 2)(x - 3) = 0 \\ form \: here \: we \: get \: x = 3 \: or \: - 2 \\ \\ x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} } } } \\ which \: state \: that \: x \: is \: always \: positive \: so \: \\ - 2 \: is \: not \: possible \\ \\ \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6} } } } = 3$

Answer 2

Answer:

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