Which one is a greater in quantity: Number System

Question

$x$ and $y$ are non-negative integers.

Then which one is greater or both are equal: $$ \sqrt{x} + \sqrt{y} \text{ or } \sqrt{x+y}? $$

Answer 1

$\sqrt x+\sqrt y$ will be $\ge\sqrt{x+y}$

iff $(\sqrt x+\sqrt y)^2\ge (\sqrt{x+y})^2$

iff $x+y+2\sqrt{xy}\ge x+y$

if $\sqrt{xy}\ge 0$ which is true

The equality occurs if at least one of $x,y$ is $0$