Rewrite the square root of the division $\sqrt{\frac{125}{8}}$ as the division of square roots $\frac{\sqrt{125}}{\sqrt{8}}$.
$$\frac{\sqrt{125}}{\sqrt{8}}$$
Factor $125=5^{2}\times 5$. Rewrite the square root of the product $\sqrt{5^{2}\times 5}$ as the product of square roots $\sqrt{5^{2}}\sqrt{5}$. Take the square root of $5^{2}$.
$$\frac{5\sqrt{5}}{\sqrt{8}}$$
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 $2^{2}$.
$$\frac{5\sqrt{5}}{2\sqrt{2}}$$
Rationalize the denominator of $\frac{5\sqrt{5}}{2\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
