# How do you simplify 5/(sqrt3) by rationalizing the denominator?

Apr 3, 2015

$\sqrt{3}$ is not a rational number.
We have been asked to write a fraction equal to this one, but with a rational number for its denominator.

Use the facts that
(1) multiplying by one may change the way a number is written, but it does not change the value of the number and
(2) $\sqrt{3} \cdot \sqrt{3} = 3$

$\frac{5}{\sqrt{3}} = \frac{5}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{5 \sqrt{3}}{\sqrt{3} \sqrt{3}} = \frac{5 \sqrt{3}}{3}$

$3$ is a rational number (in fact it is an integer).