Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 679: 61

$d\approx3.464 \text{ units} $

Using $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ or the Distance Formula, the distance, $d$, between the given points, $\left( -\sqrt{6},\sqrt{6} \right) \text{ and } \left( 0,0 \right),$ is \begin{array}{l}\require{cancel} d=\sqrt{ \left(-\sqrt{6}-0 \right)^2+\left(\sqrt{6}-0 \right)^2} \\\\ d=\sqrt{ \left( -\sqrt{6} \right)^2+\left( \sqrt{6} \right)^2} \\\\ d=\sqrt{ 6+6} \\\\ d=\sqrt{ 12} \\\\ d\approx3.464 \text{ units} .\end{array}