Đáp án:
$\begin{array}{l}
a)5 - \sqrt 8 > 5 - \sqrt 9 = 5 - 3 = 2\\
\sqrt 3 < \sqrt 4 = 2\\
\Leftrightarrow \sqrt 3 < 2 < 5 - \sqrt 8 \\
\Leftrightarrow \sqrt 3 < 5 - \sqrt 8 \\
b)5\sqrt 3 - 4 = \sqrt {75 - 2.5\sqrt 3 .4 + 16} \\
= \sqrt {91 - 40\sqrt 3 } \\
= \sqrt {91 - \sqrt {4800} } \\
3\sqrt 5 = \sqrt {45} = \sqrt {91 - 46} \\
= \sqrt {91 - \sqrt {2116} } \\
> \sqrt {91 - \sqrt {4800} } \\
\Leftrightarrow 5\sqrt 3 - 4 < 3\sqrt 5 \\
c)5\sqrt {32} = 5.\sqrt {16.2} = 5.4.\sqrt 2 = 20\sqrt 2 \\
10\sqrt 8 = 10.\sqrt {4.2} = 10.2\sqrt 2 = 20\sqrt 2 \\
\Leftrightarrow 5\sqrt {32} = 10\sqrt 8 \\
d)\\
\sqrt {3 + 2\sqrt 2 } = \sqrt {2 + 2\sqrt 2 + 1} = \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} \\
= \sqrt 2 + 1\\
\Leftrightarrow 1 + \sqrt 2 = \sqrt {3 + 2\sqrt 2 }
\end{array}$
