what is the following quotient?\n$\frac{sqrt{96}}{sqrt{8}}$\n$2sqrt{3}$\n$4$\n$2sqrt{22}$\n$12$

Explanation:

Step1: Simplify square - roots

We know that $\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}$ and $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$. So the expression $\frac{\sqrt{96}}{\sqrt{8}}$ becomes $\frac{4\sqrt{6}}{2\sqrt{2}}$.

Step2: Simplify the fraction

$\frac{4\sqrt{6}}{2\sqrt{2}}=\frac{4}{2}\times\frac{\sqrt{6}}{\sqrt{2}} = 2\times\frac{\sqrt{6}}{\sqrt{2}}$.

Step3: Rationalize the denominator

$\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{\frac{6}{2}}=\sqrt{3}$. Then $2\times\frac{\sqrt{6}}{\sqrt{2}}=2\sqrt{3}$.

Answer:

$2\sqrt{3}$