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

Mar 6, 2017

$5 \sqrt{6 {x}^{17}} = 5 \sqrt{6} {x}^{\frac{17}{2}}$ assuming $x$ is positive,

otherwise $\frac{5 \sqrt{6} \sqrt{{x}^{18}}}{\sqrt{x}}$

#### Explanation:

Use the square root property: $\frac{\sqrt{m}}{\sqrt{n}} = \sqrt{\frac{m}{n}}$

$\frac{\sqrt{300 {x}^{18}}}{\sqrt{2 x}} = \sqrt{\frac{300 {x}^{18}}{2 x}} = \sqrt{\frac{150 {x}^{18}}{x}}$

Use the exponent rules: ${x}^{m} / {x}^{n} = {x}^{m - n}$ and ${x}^{m} {x}^{n} = {x}^{m + n}$

$\sqrt{\frac{150 {x}^{18}}{x}} = \sqrt{150 {x}^{17}}$

Use the square root property: $\sqrt{m \cdot n} = \sqrt{m} \sqrt{n}$

$= \sqrt{25 \cdot 6 {x}^{17}} = \sqrt{25} \sqrt{6} \sqrt{{x}^{17}}$

$= 5 \sqrt{6 {x}^{17}}$

Remember that $\sqrt{m} = {m}^{\frac{1}{2}}$

So $5 \sqrt{6 {x}^{17}} = 5 \sqrt{6} {x}^{\frac{17}{2}}$