Factor $580=2^{2}\times 145$. Rewrite the square root of the product $\sqrt{2^{2}\times 145}$ as the product of square roots $\sqrt{2^{2}}\sqrt{145}$. Take the square root of $2^{2}$.
$$\frac{2\sqrt{145}}{2^{2}\sqrt{2222}}$$
Calculate $2$ to the power of $2$ and get $4$.
$$\frac{2\sqrt{145}}{4\sqrt{2222}}$$
Cancel out $2$ in both numerator and denominator.
$$\frac{\sqrt{145}}{2\sqrt{2222}}$$
Rationalize the denominator of $\frac{\sqrt{145}}{2\sqrt{2222}}$ by multiplying numerator and denominator by $\sqrt{2222}$.
