Divide Square Roots: example 9.66

To rationalize a denominator, we can multiply a square root by itself. To keep the fraction equivalent, we multiply both the numerator and denominator by the same factor.

$\begin{array}{cccc}& & & \frac{4}{\sqrt{3}}\hfill \\ \\ \\ \text{Multiply both the numerator and denominator by}\sqrt{3}.\hfill & & & \frac{4·\sqrt{3}}{\sqrt{3}·\sqrt{3}}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & \frac{4\sqrt{3}}{3}\hfill \end{array}$