Rewrite the square root of the division $\sqrt{\frac{85}{48}}$ as the division of square roots $\frac{\sqrt{85}}{\sqrt{48}}$.
$$\frac{\sqrt{85}}{\sqrt{48}}$$
Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
$$\frac{\sqrt{85}}{4\sqrt{3}}$$
Rationalize the denominator of $\frac{\sqrt{85}}{4\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.
