Use the distributive property to multiply $\sqrt{555}+25$ by $\sqrt{222}$.
$$\frac{\sqrt{555}\sqrt{222}+25\sqrt{222}}{888}$$
To multiply $\sqrt{555}$ and $\sqrt{222}$, multiply the numbers under the square root.
$$\frac{\sqrt{123210}+25\sqrt{222}}{888}$$
Factor $123210=111^{2}\times 10$. Rewrite the square root of the product $\sqrt{111^{2}\times 10}$ as the product of square roots $\sqrt{111^{2}}\sqrt{10}$. Take the square root of $111^{2}$.
