Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 56: 20

$\sqrt{6}$

We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this along with the root rule for limits, we have $\lim\limits_{z \to 4}\sqrt{z^2-10}=\sqrt{4^2-10}=\sqrt{16-10}=\sqrt{6}.$