Question

$\sqrt{7 \sqrt{7 \sqrt{7..... \infty } } }$
Can any one give step by step explanation ..

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Answer 1

$\huge \bold {\red {\underline{ \underline{\mathfrak{ANSWER}}}}} \red{ :}$

$\star \: \: \underline \blue{Solution} \blue{:-}$

$\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7...} } } } = x \bold{(let)} \\ \longrightarrow \: 7\sqrt{7 \sqrt{7 \sqrt{7...} } } = {x}^{2} \bold{[square \ both \ side]} \\ \longrightarrow7x = {x}^{2} \bold{[as \: x = \sqrt{7 \sqrt{7 \sqrt{7...} } } ]} \\ \longrightarrow {x }^{2} - 7x = 0 \\ \longrightarrow x(x - 7) = 0 \\ \\ \mathfrak {\bold{\boxed{x = 0 \: \: \: \: \: or \: \: \: \: \: x = 7}}}$

$\bold {\bold{\boxed {\boxed{///MARK \: IT \: BRAINLIEST///}}}}$