Answer
Zeros: $ 2 \sqrt{2},-2 \sqrt{2}$
$x$-intercepts: $ 2 \sqrt{2},-2 \sqrt{2}$
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $f(x)=0$:
$$x^2-8=0$$
Using the Square Root Method
$$x^2=8$$
$$ x = \pm \sqrt{8}$$
$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \sqrt{2}$
$$ x = \pm 2 \sqrt{2}$$
$\therefore x = 2 \sqrt{2} \text{ or } x = -2 \sqrt{2}$