Answer
$4$
Work Step by Step
We will use the following limit rules for this problem:
$ \ Rule -\ 1 \ : \lim\limits_{x \to a} [A(x)]^n =[\lim\limits_{x \to a} A(x)]^n $
$\ Rule \ - \ 2 : \lim\limits_{x \to a} A(x)=A(a)$
Applying these rules, we have:
$\lim\limits_{x\to 3}(\sqrt {x^2+7})=[\lim\limits_{x\to 3}\sqrt {x^2+7}]\\=\sqrt {(3)^2+7} \\=\sqrt {16}\\=4$
