Every function is a relation, so if you're allowed to choose only one answer then the question itself has problems.
As for whether "the square root" describes a function. It depends on the definition of "the square root" that you've been given. If I see the phrase "the square root" instead of "a square root", then I'd conclude that "the" implied a single value and that "the square root" is indeed a function. Not everyone will come to the same conclusion.
It's really not much of an issue. If your teacher says it's a "relation" then (s)he is thinking of what I'd call "a square root" where either -2 or 2 could be a square root of 4. Make a mental note of that and move on.
Personally, I put "the square root" in the same category as inverse trigonometric operations, and use the same resolution: When there are two or more answers, pick a principal value. Often, if the difference is important, as mathematical writer will use more specific language like "the principal square root" or "the square root function".
The majority use of the radical symbol √ is that principal value function, where the result is never negative. Look up "the quadratic formula" in any reference book and you're almost see something like:
x = [-b ± √(b² - 4ac)] / (2a)
If the √ were intended to represent a two-valued relation, there'd be no need for that ± symbol!