# What is x = sqrt(2sqrt(2sqrt(2sqrt(2...)))) ?

Mar 12, 2017

#### Answer:

$x = 2$

#### Explanation:

Given:

$x = \sqrt{2 \sqrt{2 \sqrt{2. . .}}}$

Square both sides to get:

${x}^{2} = 2 \sqrt{2 \sqrt{2 \sqrt{2. . .}}} = 2 x$

So either $x = 0$, which it obviously is not, or we can divide both ends by $x$ to get:

$x = 2$