Question

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

Step-by-step explanation:

▶ Question :-

→ Simplify :-

$\sf \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{6 ... \infty } } } } .$

▶ Answer :-

→ 6.

▶ Step-by-step explanation :-

$\begin{lgathered}\sf Let \: x = \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{6.... \infty } } } } . \\ \\ \sf \implies x = \sqrt{6 \bigg( \sqrt{6 \sqrt{6 \sqrt{6... \infty } } } \bigg) } \\ \\ \sf \implies x = \sqrt{6 x} . \\ \\ \{ \tt squaring \: both \: side \} \\ \\ \sf \implies {x}^{2} = 6 x.\end{lgathered}$

⇒ x² - 6x = 0 .

⇒ x( x - 6 ) = 0 .

⇒ x - 6 = 0/x .

⇒ x - 6 = 0 .

∴ x = 6 .

$\orange{ \boxed{ \sf \therefore \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{6... \infty } } } } = 6.}}$

Hence, it is solved.

Answer 2

$\huge\mathfrak\pink{Answer:-}$

→ 6.

Step-by-step explanation :-

{squaring both side}

⇒ x² - 6x = 0 .

⇒ x( x - 6 ) = 0 .

⇒ x - 6 = 0/x .

⇒ x - 6 = 0 .

∴ x = 6 .

$\huge\mathfrak\pink{Solved}$