[spicyj]

Any positive number has two square roots, but the (present-day) notational convention is always to take the positive square root.

[sid0]

Indeed, and I think the reason it's done is simply to make square-root an easy-to-deal-with single-valued function rather than a multifunction. Remember the quadratic formula: the ± in it is in addition to the square root, not part of it.