The function returns a number $y$ such that $y^2=x$: \[ f(x) = \sqrt{x} \equiv x^{\frac{1}{2}} . \]

The graph of the square root function looks like this:

{{ :math:sqrt_of_x.jpg?500 |The graph of the function $\sqrt{x}$.}}

• The inverse of $x^2$.
• Since there is no real number $y$ such that

$y^2$ is negative, the function $f(x)=\sqrt{x}$

  is not defined for negative inputs $x$.

• $2$: the degree of the root operation. More generally

you can have $n$th root $\sqrt[n]{x}$ which is the inverse

  function to $x^n$. For example, the inverse function for the 
  cubic function $f(x)=x^3$ is the //cube root//:
  \[
    f(x) = \sqrt[3]{x}  \equiv x^{\frac{1}{3}}.
  \]
  So we have $\sqrt[3]{8}=2$ since $2\times2\times2=8$.