# How do you simplify 3/ sqrt 2?

Jun 18, 2018

3/(sqrt2)=color(blue)((3sqrt2)/2

#### Explanation:

Simplify:

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

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$.

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

Apply rule: $\sqrt{a} \sqrt{a} = a$

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

Jun 18, 2018

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

#### Explanation:

It is considered good mathematical practice if you do not have any roots in the denominator. So lets 'get rid' of it!

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

$\textcolor{g r e e n}{\frac{3}{\sqrt{2}} \textcolor{red}{\times 1} \textcolor{w h i t e}{\text{ddd")->color(white)("ddd")3/sqrt2color(red)(xxsqrt2/sqrt2)color(white)("d")=color(white)("d}} \frac{3 \sqrt{2}}{2}}$