Is the inequality $(\sqrt{x} - \sqrt{y})^2 \geqslant 0$ always true for $x,y \in \mathbb{R}^+$?

Question

Suppose $x,y \in \mathbb{R}^+$

Then is the following inequality true?

$(\sqrt{x} - \sqrt{y})^2 \geqslant 0$

If it is not true then please provide an example of why it fails.

Answer 1

Since $x,y \in \mathbb{R}^+$

$\sqrt{x}$ and $\sqrt{y}$ are $\in \mathbb{R}^+$

So $\sqrt{x}-\sqrt{y}\in \mathbb{R}$

Thus $(\sqrt{x}-\sqrt{y})^2\geq0$