Question

exercises simplify the quotient. 43. \\(\frac{16}{\sqrt{24}}\\)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{24}$:
$\frac{16}{\sqrt{24}} \times \frac{\sqrt{24}}{\sqrt{24}} = \frac{16\sqrt{24}}{24}$

Step2: Simplify $\sqrt{24}$

Factor $\sqrt{24}$ into $\sqrt{4 \times 6} = 2\sqrt{6}$:
$\frac{16 \times 2\sqrt{6}}{24} = \frac{32\sqrt{6}}{24}$

Step3: Simplify the fraction

Reduce $\frac{32}{24}$ to lowest terms:
$\frac{32\div8}{24\div8}\sqrt{6} = \frac{4}{3}\sqrt{6}$

Answer:

$\frac{4\sqrt{6}}{3}$