Đáp án:
$\begin{array}{l}
\frac{{\sqrt {32} }}{{2\sqrt 6 - 2\sqrt {30} }} + \sqrt {\frac{{2\sqrt 3 }}{{4\sqrt 3 + \sqrt {45} }}} \\
= \frac{{4\sqrt 2 }}{{2\sqrt 6 \left( {1 - \sqrt 5 } \right)}} + \sqrt {\frac{{2\sqrt 3 }}{{4\sqrt 3 + 3\sqrt 5 }}} \\
= \frac{2}{{\sqrt 3 \left( {1 - \sqrt 5 } \right)}} + \sqrt {\frac{2}{{4 + \sqrt {15} }}} \\
= \frac{{2\sqrt 3 \left( {1 + \sqrt 5 } \right)}}{{3.\left( {1 - 5} \right)}} + \sqrt {\frac{{2\left( {4 - \sqrt {15} } \right)}}{{16 - 15}}} \\
= \frac{{ - \sqrt 3 \left( {1 + \sqrt 5 } \right)}}{6} + \sqrt {8 - 2\sqrt {15} } \\
= \frac{{ - \sqrt 3 \left( {1 + \sqrt 5 } \right)}}{6} + \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \frac{{ - \sqrt 3 \left( {1 + \sqrt 5 } \right)}}{6} + \sqrt 5 - \sqrt 3 \\
= \frac{{ - 7\sqrt 3 }}{6} - \frac{{\sqrt {15} }}{6} + \sqrt 5
\end{array}$
