Đáp án:
$\begin{array}{l}
a)\sqrt {8 - \sqrt {60} } - \sqrt {23 - \sqrt {240} } \\
= \sqrt {8 - 2\sqrt {15} } - \sqrt {23 - 2.2\sqrt {15} } \\
= \sqrt {{{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {2\sqrt 5 - \sqrt 3 } \right)}^2}} \\
= \sqrt 5 - \sqrt 3 - \left( {2\sqrt 5 - \sqrt 3 } \right)\\
= - \sqrt 5 \\
b)\left( {\dfrac{3}{2}\sqrt 6 + 2\sqrt {\dfrac{2}{3}} - 4\sqrt {\dfrac{3}{2}} } \right)\left( {3\sqrt {\dfrac{2}{3}} - \sqrt {12} - \sqrt 6 } \right)\\
= \left( {\dfrac{3}{2}\sqrt 6 + \dfrac{2}{3}\sqrt 6 - 2\sqrt 6 } \right).\left( {\sqrt 6 - \sqrt {12} - \sqrt 6 } \right)\\
= \dfrac{{19\sqrt 6 }}{6}.\left( { - \sqrt {12} } \right)\\
= - 19\sqrt 2 \\
c)\dfrac{4}{{\sqrt 3 + 1}} - \dfrac{5}{{\sqrt 3 - 2}} + \dfrac{6}{{\sqrt 3 - 3}}\\
= \dfrac{{4\left( {\sqrt 3 - 1} \right)}}{{3 - 1}} - \dfrac{{5\left( {\sqrt 3 + 2} \right)}}{{3 - 4}} + \dfrac{{6\left( {\sqrt 3 + 3} \right)}}{{3 - 9}}\\
= 2\sqrt 3 - 2 + 5\sqrt 3 + 10 - \sqrt 3 - 3\\
= 6\sqrt 3 + 5
\end{array}$
