Task 1. Calculate without using a calculator: $\sqrt{333^{2}+444^{2}}$.
Solution. We have

$$
\sqrt{333^{2}+444^{2}}=\sqrt{(3 \cdot 111)^{2}+(4 \cdot 111)^{2}}=\sqrt{111^{2}\left(3^{2}+4^{2}\right)}=\sqrt{111^{2} \cdot 5^{2}}=555
$$