Question

Solve this..
$\tt{} \sqrt{8 + \sqrt{8 + \sqrt{8+ \sqrt{8 + \sqrt{8 + \sqrt{8} ...} } } } } = x$
find the value of x ?​

Answer 1

perfect squares from inside the square root.

We start by factoring 757575, looking for a perfect square:

75=5\times5\times3=\blueD{5^2}\times375=5×5×3=5

2

×375, equals, 5, times, 5, times, 3, equals, start color #11accd, 5, squared, end color #11accd, times, 3.

We found one! This allows us to simplify the radical:

\begin{aligned} \sqrt{75}&=\sqrt{\blueD{5^2}\cdot3} \\\\ &=\sqrt{\blueD{5^2}} \cdot \sqrt{{3}} \\\\ &=5\cdot \sqrt{3} \end{aligned}

75

=

5

2

⋅3

=

5

2

⋅

3

=5⋅

3

So \sqrt{75}=5\sqrt{3}

75

=5

3

square root of, 75, end square root, equals, 5, square root of, 3, end square root.

Answer 2

GIVEN :-

$\tt{} \sqrt{8 + \sqrt{8 + \sqrt{8+ \sqrt{8 + \sqrt{8 + \sqrt{8} ...} } } } } = x$

SOLUTION :-

FIRSTLY ADD THE ALL :)

• THAN IT'S ANSWER WILL 16.9705627

______________________

$\huge \bold \red\longmapsto \red{16.9705627}$