# How do you simplify x *sqrt 18 - 3 * sqrt(8x^2)?

Sep 18, 2015

$x \sqrt{18} - 3 \sqrt{8 {x}^{2}} = - 3 x \sqrt{2}$
$x \sqrt{18} - 3 \sqrt{8 {x}^{2}} =$
$x \sqrt{9 \cdot 2} - 3 \sqrt{4 \cdot 2 \cdot {x}^{2}} =$
$3 x \sqrt{2} - 6 x \sqrt{2} =$
$- 3 x \sqrt{2}$
(That is, if and only if, $x \ge 0$, if not $3 x \sqrt{2} - 6 | x | \sqrt{2}$, because everything that comes out of a root must be positive or a zero.)