Question

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Find the value of :

$\sqrt {6 \sqrt{6 \sqrt{6\sqrt\cdots∞}}}$



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Answer 1

Answer:

pleaseark it as brainliest

Answer 2

Step-by-step explanation:

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$\huge\bold{Find:-} \\ \\ \sqrt {6 \sqrt{6 \sqrt{6\sqrt\cdots∞}}} \\ \\ Let...\\ \\ x = \sqrt {6 \sqrt{6 \sqrt{6\sqrt\cdots ∞}}}$

Understanding the concept which confuses students most....

$x = \sqrt {6 \sqrt{6 \sqrt{6\sqrt\cdots∞}}} \\ \\ Which \: means......\\ \\ x = \sqrt{6 \sqrt{x}}$

We have done nothing here just replaced √6√6......upto infinity to x

$x = \sqrt{6 \sqrt{x}} \\ \\ Squaring \: on \: both \: sides.... \\ \\ {x}^{2} = 6 \times \sqrt{x} \\ \\ \frac{{x}^{2}}{{x}^{\frac{1}{2}}} = 6 \\ \\ {x}^{2 - \farc{1}{2}} = 6 \\ \\ {x}^{\frac{3}{2}} = 6 \\ \\ {x}^{\frac{1}{2}} = 216 ......[ cubing \: on \: both \: sides] \\ \\ \boxed{x = 14.69 \approx 15 }$

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