1. Calculate the value of the expression:

$$
\frac{(\sqrt{666}+\sqrt{888})^{2}-\sqrt{666^{2}+888^{2}}}{444}
$$
First solution.

We calculate step by step:

$(\sqrt{666}+\sqrt{888})^{2}=$

$666+2 \cdot \sqrt{666} \cdot \sqrt{888}+888=$

$1554+2 \cdot \sqrt{6} \cdot \sqrt{111} \cdot \sqrt{8} \cdot \sqrt{111}=$

$1554+222 \sqrt{48}=$

$1554+222 \cdot 4 \sqrt{3}=$

$1554+888 \sqrt{3}$

$\sqrt{666^{2}+888^{2}}=$

$\sqrt{6^{2} \cdot 111^{2}+8^{2} \cdot 111^{2}}=\quad 1$ POINT

$\sqrt{111^{2} \cdot\left(6^{2}+8^{2}\right)}=\quad 1$ POINT

$111 \cdot \sqrt{100}=\quad 1$ POINT

1110

1 POINT

Finally:

$\frac{(\sqrt{666}+\sqrt{888})^{2}-\sqrt{666^{2}+888^{2}}}{444}=$

$\frac{1554+888 \sqrt{3}-1110}{444}=$

$\frac{444+888 \sqrt{3}}{444}=$

$1+2 \sqrt{3}$ 2 POINTS $\qquad$