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1)

\[
\sqrt{(2 - \sqrt{7})^2} = |2 - \sqrt{7}| = 2 - \sqrt{7}
\]

2)

\[
\sqrt{12} + \sqrt{75} = 2\sqrt{3} + 5\sqrt{3} = 7\sqrt{3}
\]

3)

\[
2\sqrt{18} - 7\sqrt{2} = 2 \cdot 3\sqrt{2} - 7\sqrt{2} = 6\sqrt{2} - 7\sqrt{2} = -1\sqrt{2} = -\sqrt{2}
\]

4)

\[
3\sqrt{20} - 2\sqrt{45} = 3\cdot 2\sqrt{5} - 2\cdot 3\sqrt{5} = 6\sqrt{5} - 6\sqrt{5} = 0
\]

5)

\[
\sqrt{(2\sqrt{2} + 2\sqrt{3})^2} = 2\sqrt{2} + 2\sqrt{3}
\]

6)

\[
\sqrt{25 \cdot 16} = 20
\]

7)

\[
1 - \sqrt{48} - 2\sqrt{75} = 1 - 4\sqrt{3} - 5\sqrt{3} = 1 - 9\sqrt{3}
\]

8)

\[
\sqrt{6} \cdot \sqrt{2} + 2\sqrt{2} = \sqrt{12} + 2\sqrt{2} = 2\sqrt{3} + 2\sqrt{2}
\]

9)

\[
(2\sqrt{3} - 3) + 2\sqrt{2} = 2\sqrt{3} - 3 + 2\sqrt{2}
\]