Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 18

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

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}