Is $d(x,y) = \sqrt{|x-y|}$ a metric on R?

For $x,y \in \mathbb{R}$, define $d(x,y) = \sqrt{|x-y|}$.

Is this a metric on $\mathbb{R}$?

It's clear that $d(x,x) = 0$ and $d(x,y) = d(y,x)$ for all $x,y \in \mathbb{R}$. The triangle inequality seems to hold for all values I have tested, but I have not found this function anywhere online as an example of a metric on $\mathbb{R}$.