# How do you simplify 24/sqrt(3)?

Aug 1, 2016

$8 \cdot \sqrt{3}$

#### Explanation:

Your first goal here will be to rationalize the denominator by multiplying the fraction by

$1 = \frac{\sqrt{3}}{\sqrt{3}}$

This will allow you to remove the radical term from the denominator, since

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

You thus have

$\frac{24}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{24 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{24 \cdot \sqrt{3}}{3}$

One last thing to do here -- simplify the resulting fraction by using the fact that

$24 = 12 \cdot 2 = 6 \cdot 2 \cdot 2 = 2 \cdot 2 \cdot 2 \cdot 3 = {2}^{3} \cdot 3 = 8 \cdot 3$

$\frac{8 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot \sqrt{3}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = 8 \cdot \sqrt{3}$