Answer
The domain is
$$\mathcal{D}=\left\{(x,y)|x^2+y^2\geq2^2\right\}$$ and it is sketched on th figure below
Work Step by Step
The argument of the square root has to be nonnegative so we need that $x^2+y^2-4\ge0$ which gives $x^2+y^2\ge4$, and this can be rewritten as $$x^2+y^2\geq2^2.$$
This means that the domain is geometrically the exterior of the circle with the center at the origin and with the radius of $2$ (the circle is included in this region).
So we will write for the domain
$$\mathcal{D}=\left\{(x,y)|x^2+y^2\geq2^2\right\}$$ and it is sketched on the figure below
