You can also use a lookup table, an AJAX call to a square root web service, using the canvas and drawing appropriate geometric shapes then measuring, or, if you have a bit of free time, implementing code which has commercial value, accepting money for it, and then going to Radio Shack and buying yourself a calculator with a square root key.
well the point is, and i think this is the original poster's point...questions like this are not relevant to what facebook is doing, and even if it is, its the kind of thing you look up.
In Facebook's defense (I have no affiliation with FB, and in general am not a big fan of them), they probably weren't looking for somebody to whip out Newton's method, but rather just binary search.
Everyone who says "this question is completely irrelevant" isn't completely right. This question would be completely irrelevant if they were exclusively looking for a "fancy" square root finding technique. However, binary search is a pretty basic algorithm - the trick here is to recognize that such a basic algorithm can be applied to a seemingly unrelated problem. If Facebook is testing to see if people can connect different parts of their knowledge (square root function is strictly increasing, something that everyone knows to be true at least intuitively, combined with the fact that binary search can then be used in such a situation), then it's a reasonable question to ask. Maybe not for a front-end developer though.
But personally, yeah, I'd use Math.sqrt.