Does the inequality $ \sqrt{a+b}\geq \sqrt{a/2}+\sqrt{b/2}$ have a name? This is somewhat embarrassing but if $a,b$ are nonnegative real numbers the following seems to hold
$$
\sqrt{a+b}\geq \sqrt{\frac{a}{2}}+\sqrt{\frac{b}{2}}.
$$
Does this inequality have a name?

From AM-GM
$$\frac{a+b}{2}\geq \sqrt{ab} \iff\\
a+b\geq  \frac{a+b}{2}+2\sqrt{\frac{a}{2}\cdot\frac{b}{2}} \iff\\
a+b\geq \left(\sqrt{\frac{a}{2}}+\sqrt{\frac{b}{2}}\right)^2 \overset{a,b\geq0}{\iff}\\
\sqrt{a+b}\geq \sqrt{\frac{a}{2}}+\sqrt{\frac{b}{2}}$$
Which makes it a special case or corollary of it.
