Đáp án:
$\begin{array}{l}
a)\left( {2\sqrt {20} - \dfrac{1}{3}\sqrt {45} + 2\sqrt {12} } \right)\left( {3\sqrt 5 - 4\sqrt 3 } \right)\\
= \left( {2.2\sqrt 5 - \dfrac{1}{3}.3\sqrt 5 + 2.2\sqrt 3 } \right)\left( {3\sqrt 5 - 4\sqrt 3 } \right)\\
= \left( {3\sqrt 5 + 4\sqrt 3 } \right)\left( {3\sqrt 5 - 4\sqrt 3 } \right)\\
= {\left( {3\sqrt 5 } \right)^2} - {\left( {4\sqrt 3 } \right)^2}\\
= 45 - 48\\
= - 3\\
c){\left( {\sqrt 6 + \sqrt 5 } \right)^2} + {\left( {\sqrt 6 - \sqrt 5 } \right)^2} - \dfrac{{2\sqrt 2 + 2\sqrt 3 }}{{\sqrt 2 + \sqrt 3 }}\\
= 6 + 2\sqrt {30} + 5 + 6 - 2\sqrt {30} + 5 - 2\\
= 22 - 2\\
= 20\\
d)\dfrac{4}{{\sqrt 3 + 1}} + \dfrac{1}{{\sqrt 3 - 2}} + \dfrac{6}{{\sqrt 3 - 3}}\\
= \dfrac{{4\left( {\sqrt 3 - 1} \right)}}{{3 - 1}} + \dfrac{{\sqrt 3 + 2}}{{3 - 4}} + \dfrac{{6\left( {\sqrt 3 + 3} \right)}}{{3 - 9}}\\
= 2\left( {\sqrt 3 - 1} \right) - \sqrt 3 - 2 - \sqrt 3 - 3\\
= - 7\\
e)\sqrt {14 - 8\sqrt 3 } - \sqrt {24 - \sqrt {3.144} } + \sqrt {3 - 2\sqrt 2 } \\
= \sqrt {8 - 2.2\sqrt 2 .\sqrt 6 + 6} - \sqrt {24 - 12\sqrt 3 } + \sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} \\
= \sqrt {{{\left( {2\sqrt 2 - \sqrt 6 } \right)}^2}} - \sqrt {18 - 2.3\sqrt 2 .\sqrt 6 + 6} + \sqrt 2 - 1\\
= 2\sqrt 2 - \sqrt 6 - \sqrt {{{\left( {3\sqrt 2 - \sqrt 6 } \right)}^2}} + \sqrt 2 - 1\\
= 3\sqrt 2 - \sqrt 6 - 1 - 3\sqrt 2 + \sqrt 6 \\
= - 1
\end{array}$
