Answer
Domain = $\{(x,y)|xy\geq 0\}$
(see image)
Work Step by Step
Because of the restrictions for square roots, f is defined when
$xy\geq 0$
that is, for (x,y) from the $ \mathbb{R}^{2}$ plane such that x and y have the same sign, or either is zero.
This defines the quadrants I and III, with axes included.
Domain = $\{(x,y)|xy\geq 0\}$
(see image)
