Question

What will be the solution ( with steps ) ?
$\sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5} } } }$
... infinite number​

Answer 1

$\huge\text{\underline{Answer}}$

We have to solve :-

$\implies$ $\sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5....... \infty } } } } }$

Let

$\implies$ $x = \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5... \infty } } } } }$

Now squaring on both side we get ,

$\implies$ ${x}^{2} = ( \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5..... \infty } } } } } ) ^{2}$

Now,

$\implies$ ${x}^{2} = 5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5... \infty } } } } }$

here we have taken x

$\implies$ ${x}^{2} = 5x$

$\implies$ $x = 5$