Đáp án:
$\begin{array}{l}
1)\dfrac{2}{{\sqrt 2 }} = \sqrt 2 \\
2)\dfrac{3}{{2\sqrt 5 }} = \dfrac{{3\sqrt 5 }}{{2.5}} = \dfrac{{3\sqrt 5 }}{{10}}\\
3)\dfrac{{12}}{{5\sqrt 6 }} = \dfrac{{2.6}}{{5\sqrt 6 }} = \dfrac{{2\sqrt 6 }}{5}\\
4)\dfrac{{11 + \sqrt {11} }}{{\sqrt {11} }} = \dfrac{{\sqrt {11} \left( {\sqrt {11} + 1} \right)}}{{\sqrt {11} }} = \sqrt {11} + 1\\
5)\dfrac{{5 + \sqrt 5 }}{{\sqrt 5 }} = \dfrac{{\sqrt 5 \left( {\sqrt 5 + 1} \right)}}{{\sqrt 5 }} = \sqrt 5 + 1\\
6)\dfrac{{\sqrt {15} - \sqrt {18} }}{{\sqrt 5 - \sqrt 6 }} = \dfrac{{\sqrt 3 \left( {\sqrt 5 - \sqrt 6 } \right)}}{{\sqrt 5 - \sqrt 6 }} = \sqrt 3 \\
7)\dfrac{{\sqrt 6 - \sqrt {27} }}{{3 - \sqrt 2 }} = \dfrac{{\sqrt 3 \left( {\sqrt 2 - \sqrt 9 } \right)}}{{3 - \sqrt 2 }} = - \sqrt 3 \\
8)\dfrac{{6 - 2\sqrt 5 }}{{1 - \sqrt 5 }} = \dfrac{{5 - 2\sqrt 5 + 1}}{{1 - \sqrt 5 }} = \dfrac{{{{\left( {1 - \sqrt 5 } \right)}^2}}}{{1 - \sqrt 5 }} = 1 - \sqrt 5 \\
9)\dfrac{{\sqrt 2 }}{{\sqrt 5 - 2}} = \dfrac{{\sqrt 2 \left( {\sqrt 5 + 2} \right)}}{{\left( {\sqrt 5 - 2} \right)\left( {\sqrt 5 + 2} \right)}}\\
= \dfrac{{\sqrt 2 \left( {\sqrt 5 + 2} \right)}}{{5 - 4}} = \sqrt {10} + 2\sqrt 2 \\
10)\\
\dfrac{4}{{\sqrt 5 + \sqrt 3 }} = \dfrac{{4\left( {\sqrt 5 - \sqrt 3 } \right)}}{{\left( {\sqrt 5 + \sqrt 3 } \right)\left( {\sqrt 5 - \sqrt 3 } \right)}}\\
= \dfrac{{4\left( {\sqrt 5 - \sqrt 3 } \right)}}{{5 - 3}} = 2\sqrt 5 - 2\sqrt 3
\end{array}$
