Math Problem with Cool Concept

What's x = √1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1+√1... ?
It's a irrational number, but exactly what is it?
(algebra helps/math knowledge)

Edit, Hint: it's around 1.68