Answer
106.05 miles, 75\sqrt 2 miles
Work Step by Step
North and east have each traveled $x$ miles.
$x^2+x^2=150^2$
$2x^2=22500$
$2x^2/2=22500/2$
$x^2=11250$
We are looking for a distance, so we want the positive square root.
$\sqrt {x^2} = \sqrt {11250}$
$x=\sqrt {11250}$
$x=\sqrt {2*5625}$
$x=\sqrt 2 *\sqrt {5625}$
$x=\sqrt 2 * 75$
$x=75*\sqrt 2$
$\sqrt 2 = 1.414$
$75*1.414 = 106.05$
