# How do you rationalize sqrt(14/x)?

May 29, 2018

$\frac{\sqrt{14 x}}{x}$

$x \ne 0$

#### Explanation:

$= \sqrt{\frac{14}{x}}$

Assume $x \ne 0$

$= \frac{\sqrt{14}}{\sqrt{x}}$

$= \frac{\sqrt{14}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

$= \frac{\sqrt{14 x}}{x}$

May 29, 2018

See a solution process below:

#### Explanation:

First, multiply the term under the radical by the appropriate form of $1$:

$\sqrt{\frac{x}{x} \cdot \frac{14}{x}} \implies$

$\sqrt{\frac{14 x}{x} ^ 2}$

Next, use this rule for radicals to simplify the expression:

$\sqrt{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}} = \frac{\sqrt{\textcolor{red}{a}}}{\sqrt{\textcolor{b l u e}{b}}}$

$\sqrt{\frac{\textcolor{red}{14 x}}{\textcolor{b l u e}{{x}^{2}}}} \implies$

$\frac{\sqrt{\textcolor{red}{14 x}}}{\sqrt{\textcolor{b l u e}{{x}^{2}}}} \implies$

$\frac{\sqrt{\textcolor{red}{14 x}}}{\textcolor{b l u e}{x}}$