Factor $500=10^{2}\times 5$. Rewrite the square root of the product $\sqrt{10^{2}\times 5}$ as the product of square roots $\sqrt{10^{2}}\sqrt{5}$. Take the square root of $10^{2}$.
$$\frac{10\sqrt{5}}{\sqrt{75}}$$
Factor $75=5^{2}\times 3$. Rewrite the square root of the product $\sqrt{5^{2}\times 3}$ as the product of square roots $\sqrt{5^{2}}\sqrt{3}$. Take the square root of $5^{2}$.
$$\frac{10\sqrt{5}}{5\sqrt{3}}$$
Cancel out $5$ in both numerator and denominator.
$$\frac{2\sqrt{5}}{\sqrt{3}}$$
Rationalize the denominator of $\frac{2\sqrt{5}}{\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.
