#### Answer

$z=\pm\dfrac{\sqrt{10}}{5}$

#### Work Step by Step

Using the properties of equality, the given equation, $
5z^2-2=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
5z^2=2
\\\\
z^2=\dfrac{2}{5}
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
z=\pm\sqrt{\dfrac{2}{5}}
\\\\
z=\pm\sqrt{\dfrac{2}{5}\cdot\dfrac{5}{5}}
\\\\
z=\pm\sqrt{\dfrac{10}{25}}
\\\\
z=\pm\dfrac{\sqrt{10}}{\sqrt{25}}
\\\\
z=\pm\dfrac{\sqrt{10}}{(5)^2}
\\\\
z=\pm\dfrac{\sqrt{10}}{5}
.\end{array}