Answer
$5$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to -4}\sqrt {x^2+9}=\sqrt {(-4)^2+9}=\sqrt{16+9}=5$
