Answer
$\lim\limits_{z \to 4}\sqrt {z^{2}-10} =\sqrt 6 $ = 2.449
Work Step by Step
First we will calculate the limit of: $f(x) = (z^{2}-10)$
$\lim\limits_{z \to 4}(z^{2}-10) = \lim\limits_{z \to 4}z^{2} -\lim\limits_{z \to 4}10$
$ = 16 -10$
$ = 6$
Now, applying the limits property:
$\lim\limits_{z \to 4}\sqrt (z^{2}-10) =\sqrt 6 $ = 2.449
