Why the plot of $\sqrt{x}$ has no negative part??

Question

We all know that for every real and positive number $N$ we have

$$\sqrt{N} = \pm a$$

for example $\sqrt{25} = \pm 5$.

Now: why the plot of the function $\sqrt{x}$ has only a positive part in the Cartesian plane? I have two results, plus and minus a certain number, so why the plot takes into account only the positive results?

Answer 1

By definition $\sqrt{x}$ indicates the positive (or principal) square root of $x$. If we want indicate all the two root we have to write explicitly $\pm\sqrt{x}$.

Answer 2

Actually, the function $f(x)=\sqrt{x}$ usually refers to the principal square root which is defined as the nonnegative solution to $r^2=x$ for $x\ge0$.

While it's true that in general there are two solutions to the equation $r^2=x$, we really like single valued functions.

Answer 3

The √ symbol is used to denote the principal square root of a number, i.e. the positive one.