Question

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

Answer 1

`x=2`

Explanation:

Given:

`x = sqrt(2sqrt(2sqrt(2...)))`

Square both sides to get:

`x^2 = 2sqrt(2sqrt(2sqrt(2...))) = 2x`

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

`x = 2`