Đáp án:
$\begin{array}{l}
D = \frac{{\sqrt {10} + \sqrt 6 }}{{2\sqrt 5 + \sqrt {12} }} = \frac{{\sqrt 2 \left( {\sqrt 5 + \sqrt 3 } \right)}}{{2\sqrt 5 + 2\sqrt 3 }} = \frac{{\sqrt 2 \left( {\sqrt 5 + \sqrt 3 } \right)}}{{2\left( {\sqrt 5 + \sqrt 3 } \right)}} = \frac{{\sqrt 2 }}{2}\\
E = \frac{1}{{\sqrt 5 - \sqrt 7 }} + \frac{1}{{\sqrt 5 + \sqrt 7 }}\\
= \frac{{\sqrt 5 + \sqrt 7 + \sqrt 5 - \sqrt 7 }}{{\left( {\sqrt 5 + \sqrt 7 } \right)\left( {\sqrt 5 - \sqrt 7 } \right)}}\\
= \frac{{2\sqrt 5 }}{{5 - 7}}\\
= - \sqrt 5 \\
C = \sqrt {7 - 4\sqrt 3 } - \sqrt {7 + 4\sqrt 3 } \\
= \sqrt {4 - 2.\sqrt 3 .2 + 3} - \sqrt {4 + 2.\sqrt 3 .2 + 3} \\
= \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} \\
= 2 - \sqrt 3 + 2 + \sqrt 3 \\
= 4\\
F = \sqrt {{{\left( {\sqrt 7 - 5} \right)}^2}} + \sqrt {{{\left( {2 - \sqrt 7 } \right)}^2}} \\
= 5 - \sqrt 7 + \sqrt 7 - 2\\
= 3
\end{array}$
