Question

14 rationalize the denominator and enter answer in simplest form. $\frac{4}{3sqrt{6}}$

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $\sqrt{6}$ to rationalize:
$\frac{4}{3\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{4\sqrt{6}}{3 \times (\sqrt{6})^2}$

Step2: Simplify the denominator

Calculate $(\sqrt{6})^2 = 6$, so:
$\frac{4\sqrt{6}}{3 \times 6} = \frac{4\sqrt{6}}{18}$

Step3: Reduce the fraction

Divide numerator and denominator by their GCD (2):
$\frac{4\sqrt{6} \div 2}{18 \div 2} = \frac{2\sqrt{6}}{9}$

Answer:

$\frac{2\sqrt{6}}{9}$