which is equivalent to $\frac{sqrt{3}}{sqrt{8}}$ when the denominator is \rationalized\?\na…

which is equivalent to $\frac{sqrt{3}}{sqrt{8}}$ when the denominator is \rationalized\?\na. $\frac{3}{8}$\nb. $\frac{sqrt{6}}{4}$\nc. $\frac{sqrt{3}}{8}$\nd. $\frac{sqrt{24}}{64}$\ne. $\frac{8sqrt{3}}{3}$

which is equivalent to $\frac{sqrt{3}}{sqrt{8}}$ when the denominator is \rationalized\?\na. $\frac{3}{8}$\nb. $\frac{sqrt{6}}{4}$\nc. $\frac{sqrt{3}}{8}$\nd. $\frac{sqrt{24}}{64}$\ne. $\frac{8sqrt{3}}{3}$

Answer

Explanation:

Step1: Rationalize the denominator

Multiply the fraction $\frac{\sqrt{3}}{\sqrt{8}}$ by $\frac{\sqrt{8}}{\sqrt{8}}$. So we have $\frac{\sqrt{3}\times\sqrt{8}}{\sqrt{8}\times\sqrt{8}}$.

Step2: Simplify the numerator and denominator

For the numerator, $\sqrt{3}\times\sqrt{8}=\sqrt{3\times8}=\sqrt{24}=\sqrt{4\times6} = 2\sqrt{6}$. For the denominator, $\sqrt{8}\times\sqrt{8}=8$. Then the fraction becomes $\frac{2\sqrt{6}}{8}=\frac{\sqrt{6}}{4}$.

Answer:

B. $\frac{\sqrt{6}}{4}$