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?

A little late in the game but i think i can make a valid point. 
The square root is a function, since people did go through all the trouble of finding a derivative for it,  and the definition of a function is that is a unique mapping between the an element of the set of inputs and an element of the set of outputs. 
Now if the idea proposed by the textbooks would be that square root is not a function because one element of the input say 4 actually maps itself to two elements of the output set which is false. But the square of -2 is actually 4 so we have a small problem. 
The answer comes from a more general definition of the square root which is $\sqrt{x^2}$ is the absolute value of x, which works just great. Now the absolute value of -2 is 2 so there is no longer any need for debate because $\sqrt{(-2)^2}=|-2| = 2$ which solves any misconception
