# How do you rationalize the denominator and simplify 3/sqrt12?

Mar 20, 2016

$= \frac{\sqrt{12}}{4}$

#### Explanation:

$\frac{3}{\sqrt{12}}$

(3 * color(blue)(sqrt12))/(( sqrt12 * color(blue)( sqrt12))

$= \frac{\left(3 \sqrt{12}\right)}{12}$

$= \frac{\cancel{3} \sqrt{12}}{\cancel{12}}$

$= \frac{\sqrt{12}}{4}$

Mar 20, 2016

Bit more explanation

$= \frac{\sqrt{12}}{4}$

#### Explanation:

If you multiply a value by 1 you do not change its intrinsic value.

The thing is, 1 can come in many forms. For example$\text{ } \frac{3}{3}$.

So you can write 1 as $1 = \frac{\sqrt{12}}{\sqrt{12}}$

Given:$\text{ } \frac{3}{\sqrt{12}}$

Multiply by 1 but in the form $1 = \frac{\sqrt{12}}{\sqrt{12}}$

$\text{ } \frac{3}{\sqrt{12}} \times \frac{\sqrt{12}}{\sqrt{12}}$

$= \frac{3 \times \sqrt{12}}{\sqrt{12} \times \sqrt{12}}$

$= \frac{3 \sqrt{12}}{12}$

Divide top and bottom by 3

$= \frac{3 \sqrt{12} \div 3}{12 \div 3}$

$= \frac{\sqrt{12}}{4}$

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$\textcolor{red}{\text{If you really wanted to be absolutely correct about the answer }}$
$\textcolor{red}{\text{consider this:}}$

$\sqrt{12}$ is a number that when multiplied by itself results in +12

However$\sqrt{12}$ could be negative. Think about:

$\left(- 3\right) \times \left(- 3\right) = + 9 = \left(+ 3\right) \times \left(+ 3\right)$

$\textcolor{g r e e n}{\pm \frac{\sqrt{12}}{4}}$
$\textcolor{red}{\text{No!}}$
The question gives: $\frac{\sqrt{12}}{4}$
The absence of any sign means that it is positive. Consequently the questions single $\sqrt{12}$ is positive. So the solutions single $\sqrt{12}$ has to be positive as well.