General misconception about $\sqrt x$ I noticed a large portion of general public (who knows what square root is) has a different concept regarding the surd of a positive number, $\sqrt\cdot$, or the principal square root function.
It seems to me a lot of people would say, for example, $\sqrt 4 = \pm 2$, instead of $\sqrt 4 = 2$. People even would correct a statement of the latter form to one with a $\pm$ sign. Some also claim that, since $2^2 = 4$ and $(-2)^2 = 4$, $\sqrt 4 = \pm 2$. Some people continue to quote other "evidences" like the $y=x^2$ graph. While most people understand there are two square roots for a positive number, some seem to have confused this with the surd notation.
From an educational viewpoint, what might be lacking when teaching students about surd forms? Is a lack of understanding to functions a reason for this misconception?

Now I have noticed another recent question that hinted that poster was confused. Following @AndréNicolas's comment below, might these confusion really come from two different communities using the same symbol?

The square root of $x$ is a number which when squared gives $x$. For $16$ there are two such numbers, so there are two square roots of $16$. For $0$, there is one and for any negative number there is none.
Now, simply call the non-negative square root of a number, the principal square root. There is only one such number for all non-negative numbers and thus, the principal square root of a number is unambiguous (unless the number is negative, in which case it is undefined).
We denote the principal square root of $x\geq0$ as $\sqrt{x}$. The other square root is then $-\sqrt x$. So, we can say that the square roots of $2$ are $\sqrt{2}$ and $-\sqrt{2}$ and of $16$ are $\sqrt{16}(=4)$ and $-\sqrt{16}=(-4)$.
I think the reason some people may have confusion with this is that they don't understand/know that $\sqrt{x}$ is used to denote the non-negative square root and nothing else.
