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

Question

2003 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-12T00:16:30

$x=2$

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:

$x = 2$

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