Đáp án:
$\begin{array}{l}
a)\dfrac{1}{{2\sqrt 2 + \sqrt 7 }} + \sqrt {175} - \dfrac{{6\sqrt 2 - 4}}{{3 - \sqrt 2 }}\\
= \dfrac{{2\sqrt 2 - \sqrt 7 }}{{8 - 7}} + \sqrt {25.7} - \dfrac{{2\sqrt 2 \left( {3 - \sqrt 2 } \right)}}{{3 - \sqrt 2 }}\\
= 2\sqrt 2 - \sqrt 7 + 5\sqrt 7 - 2\sqrt 2 \\
= 4\sqrt 7 \\
b)\dfrac{{\sqrt {15} + \sqrt 3 }}{{\sqrt 5 + 1}} - \dfrac{2}{{\sqrt 3 - 1}}\\
= \dfrac{{\sqrt 3 \left( {\sqrt 5 + 1} \right)}}{{\sqrt 5 + 1}} - \dfrac{{2\left( {\sqrt 3 + 1} \right)}}{{3 - 1}}\\
= \sqrt 3 - \left( {\sqrt 3 + 1} \right)\\
= - 1\\
c)\sqrt {29 - 12\sqrt 5 } - \sqrt {14 - 6\sqrt 5 } \\
= \sqrt {20 + 2.2\sqrt 5 .3 + 9} - \sqrt {9 - 2.3.\sqrt 5 + 5} \\
= \sqrt {{{\left( {2\sqrt 5 + 3} \right)}^2}} - \sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} \\
= 2\sqrt 5 + 3 - \left( {3 - \sqrt 5 } \right)\\
= 3\sqrt 5 \\
d)3\sqrt {24} - \dfrac{1}{3}\sqrt {54} - 10\sqrt {\dfrac{3}{2}} \\
= 3.2\sqrt 6 - \dfrac{1}{3}.3\sqrt 6 - 10.\dfrac{{\sqrt 6 }}{2}\\
= 6\sqrt 6 - \sqrt 6 - 5\sqrt 6 \\
= 0\\
e)\dfrac{1}{{2\sqrt 3 + 3}} + \dfrac{1}{{2\sqrt 3 - 3}}\\
= \dfrac{{2\sqrt 3 - 3 + 2\sqrt 3 + 3}}{{\left( {2\sqrt 3 + 3} \right)\left( {2\sqrt 3 - 3} \right)}}\\
= \dfrac{{4\sqrt 3 }}{{12 - 9}}\\
= \dfrac{{4\sqrt 3 }}{3}
\end{array}$
