How do you rationalize the denominator and simplify 6/(sqrt(2x))?

Apr 1, 2018

$\frac{3 \sqrt{2 x}}{x}$

Explanation:

$\frac{6}{\sqrt{2 x}}$
$\frac{6}{\sqrt{2 x}} \cdot \left[\frac{\cancel{-} \sqrt{2 x}}{\cancel{-} \sqrt{2 x}}\right]$
which will give,
$\frac{\cancel{6} \sqrt{2 x}}{\cancel{2} x} = \frac{3 \sqrt{2 x}}{x}$

Apr 1, 2018

$\frac{3 \sqrt{2 x}}{x}$

Explanation:

$\text{note that } \sqrt{a} \times \sqrt{a} = a$

$\text{to rationalise the denominator, that is eliminate the}$
$\text{radical from the denominator then}$

$\text{multiply numerator/denominator by } \sqrt{2 x}$

$\Rightarrow \frac{6}{\sqrt{2 x}} \times \frac{\sqrt{2 x}}{\sqrt{2 x}}$

$= \frac{6 \sqrt{2 x}}{2 x} = \frac{3 \sqrt{2 x}}{x}$