# How do I divide and simplify sqrt(300x^18)/sqrt(2x)?

$5 \cdot \sqrt{6} \cdot {x}^{8} \sqrt{x}$
$\frac{\sqrt{300 {x}^{18}}}{\sqrt{2 x}} = \sqrt{\frac{300 {x}^{18}}{2 x}} = \sqrt{150 {x}^{17}} = \sqrt{25 \cdot 6 {x}^{17}} = 5 \sqrt{6 {x}^{17}} = 5 \cdot \sqrt{6} \cdot \sqrt{{x}^{17}} = 5 \cdot \sqrt{6} \cdot {x}^{8} \sqrt{x}$