# How do you rationalize the denominator and simplify 3/sqrt2?

Apr 4, 2017

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

#### Explanation:

To rationalise the denominator, you must multiply the whole fraction (top and bottom) by the denominator. The goal is to eliminate roots in the denominator.

so,

$\frac{3}{\sqrt{2}} = \frac{3 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}$

simplifying,

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

Reminder,

$\sqrt{2} \cdot \sqrt{2} = {\left(\sqrt{2}\right)}^{2} = 2$