Answer
$4$
Work Step by Step
$\lim\limits_{(x,y) \to (2,2)} \dfrac{(x+y)-4}{\sqrt {x+y}-2}=\lim\limits_{(x,y) \to (2,2)} \dfrac{(\sqrt{x+y})^2-(2)^2}{\sqrt {x+y}-2}$
This implies that$\lim\limits_{(x,y) \to (2,2)} \dfrac{(\sqrt{x+y})-2)(\sqrt{x+y}+2)}{\sqrt {x+y}-2}=\lim\limits_{(x,y) \to (2,2)}(\sqrt{x+y}+2)$
Thus, we get $2+2=4$
