# How do you rationalize 12/sqrt13?

May 17, 2018

See a solution process below:

#### Explanation:

To rationalize a fraction we need to multiply the fraction by the appropriate form of $1$ to eliminate the radical in the denominator:

$\frac{12}{\sqrt{13}} \implies \frac{\sqrt{13}}{\sqrt{13}} \times \frac{12}{\sqrt{13}} \implies \frac{12 \sqrt{13}}{\sqrt{13}} ^ 2 \implies \frac{12 \sqrt{13}}{13}$

May 17, 2018

It becomes $\frac{12 \cdot \sqrt{13}}{13}$

#### Explanation:

To get this, you need to understand that $\sqrt{13} \cdot \sqrt{13} = 13$.

So you want to multiply the entire fraction by $\frac{\sqrt{13}}{\sqrt{13}}$ which will remove the surd (square root) from the denominator, moving it to the numerator i.e. $\left(\frac{12}{\sqrt{13}}\right) \cdot \frac{\sqrt{13}}{\sqrt{13}} = \frac{12 \cdot \sqrt{13}}{13}$.

Hope this helps.