How do you rationalize $\sqrt{\frac{14}{x}}$ $sqrt(14/x)$ ?

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Answer 1 · 2018-05-29T17:15:55

$\frac{\sqrt{14 x}}{x}$ $(sqrt(14x))/x$

$x \neq 0$ $x!=0$

$= \sqrt{\frac{14}{x}}$ $=sqrt(14/x)$

Assume $x \neq 0$ $x!=0$

$= \frac{\sqrt{14}}{\sqrt{x}}$ $=sqrt14/sqrtx$

$= \frac{\sqrt{14}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$ $=sqrt14/sqrtx*sqrtx/sqrtx$

$= \frac{\sqrt{14 x}}{x}$ $=(sqrt(14x))/x$

Answer 2 · 2018-05-29T17:16:33

See a solution process below:

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

$\sqrt{\frac{x}{x} \cdot \frac{14}{x}} \Rightarrow$ $sqrt(x/x * 14/x) =>$

$\sqrt{\frac{14 x}{x^{2}}}$ $sqrt((14x)/x^2)$

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

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))$

$\sqrt{\frac{14 x}{x^{2}}} \Rightarrow$ $sqrt(color(red)(14x)/color(blue)(x^2)) =>$

$\frac{\sqrt{14 x}}{\sqrt{x^{2}}} \Rightarrow$ $sqrt(color(red)(14x))/sqrt(color(blue)(x^2)) =>$

$\frac{\sqrt{14 x}}{x}$ $sqrt(color(red)(14x))/color(blue)(x)$

How do you rationalize √14xsqrt(14/x)?