.
Let
.
Then
(after the first plus sign, there is again an infinite string of 3’s under radicals and this is precisely what x is).
Hence x2 = x + 3, so x2 - x - 3 = 0 and solving we obtain
.
Our answer is obviously positive, so in fact
.
[Note: Technically speaking, we are dealing with an infinite sequence defined recursively and we should be worried about whether the sequence converges or not, but that would entail some concepts from calculus.]