Answer
The domain is
$$\mathcal{D}=\{(x,y)|x\ge2,y\ge1\}.$$
It is presented in the figure below:
Work Step by Step
Arguments of both square roots have to be nonnegative so we get
$$x-2\geq0,\quad y-1\geq0.$$
This gives
$$x\geq2,\quad y\geq1,$$
so we can write for the domain
$$\mathcal{D}=\{(x,y)|x\geq2,y\geq1\}.$$
Geometrically, it is an infinite region of $xy$ plane that is bounded by lines $x=2$ and $y=1$, including these boundaries (rays along these lines starting from the point $(2,1)$ where they meet.) It is illustrated in the figure below
