Divide $5$ by $\frac{6}{\frac{7}{\sqrt{8}}}$ by multiplying $5$ by the reciprocal of $\frac{6}{\frac{7}{\sqrt{8}}}$.
$$\frac{5\times \frac{7}{\sqrt{8}}}{6}$$
Factor $8=2^{2}\times 2$. Rewrite the square root of the product $\sqrt{2^{2}\times 2}$ as the product of square roots $\sqrt{2^{2}}\sqrt{2}$. Take the square root of $2^{2}$.
$$\frac{5\times \frac{7}{2\sqrt{2}}}{6}$$
Rationalize the denominator of $\frac{7}{2\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
