Question

Find the distance between (0, 2 sqrt 5) and (-2 sqrt 6 , 0)

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{2\sqrt{5}})\qquad (\stackrel{x_2}{-2\sqrt{6}}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-2\sqrt{6}-0)^2+(0-2\sqrt{5})^2}\implies d=\sqrt{(-2\sqrt{6})^2+(-2\sqrt{5})^2} \\\\\\ d=\sqrt{(2^2\cdot (\sqrt{6})^2)+(2^2\cdot (\sqrt{5})^2)}\implies d=\sqrt{(4\cdot 6)+(4\cdot 5)} \\\\\\ d=\sqrt{24+20}\implies d=\sqrt{44}\implies d=\sqrt{2^2\cdot 11}\implies d=2\sqrt{11}$