Đáp án:
$\begin{array}{l}
1)\\
- 4 = - 2.2 = - 2.\left( {3 - 1} \right) = - 2.\left( {\sqrt 9 - 1} \right)\\
2 - 2\sqrt 5 = - 2.\left( {\sqrt 5 - 1} \right) > - 2\left( {\sqrt 9 - 1} \right)\\
\Leftrightarrow - 4 < 2 - 2\sqrt 5 \\
2)\\
\sqrt 2 + \sqrt 7 = \sqrt {9 + 2\sqrt {14} } = \sqrt {9 + \sqrt {56} } \\
2 + \sqrt 5 = \sqrt {9 + 4\sqrt 5 } = \sqrt {9 + \sqrt {80} } \\
\Leftrightarrow \sqrt 2 + \sqrt 7 < 2 + \sqrt 5 \\
3)\\
\sqrt {11} - \sqrt 3 = \sqrt {14 - 2\sqrt {33} } = \sqrt {14 - \sqrt {132} } \\
\sqrt 8 - \sqrt 6 = \sqrt {14 - 2\sqrt {8.6} } = \sqrt {14 - \sqrt {192} } \\
\Leftrightarrow \sqrt {11} - \sqrt 3 > \sqrt 8 - \sqrt 6 \\
4)\sqrt 3 + \sqrt {11} = \sqrt {14 + 2\sqrt {33} } = \sqrt {14 + \sqrt {132} } \\
3 + \sqrt 5 = \sqrt {14 + 6\sqrt 5 } = \sqrt {14 + \sqrt {180} } \\
\Leftrightarrow \sqrt 3 + \sqrt {11} < 3 + \sqrt 5
\end{array}$
