Đáp án:
$\begin{array}{l}
a)\sqrt {4 - 2\sqrt 3 } - \sqrt 3 \\
= \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} - \sqrt 3 \\
= \sqrt 3 - 1 - \sqrt 3 \\
= - 1\\
b)\sqrt {11 + 6\sqrt 2 } - 3 + \sqrt 2 \\
= \sqrt {{{\left( {3 + \sqrt 2 } \right)}^2}} - 3 + \sqrt 2 \\
= 3 + \sqrt 2 - 3 + \sqrt 2 \\
= 2\sqrt 2 \\
c)\sqrt {11 - 6\sqrt 2 } - \sqrt {6 - 4\sqrt 2 } \\
= \sqrt {{{\left( {3 - \sqrt 2 } \right)}^2}} - \sqrt {{{\left( {2 - \sqrt 2 } \right)}^2}} \\
= 3 - \sqrt 2 - \left( {2 - \sqrt 2 } \right)\\
= 1\\
d)\sqrt {11 - 6\sqrt 3 } + \sqrt {13 - 4\sqrt 3 } \\
= \sqrt {11 - 6\sqrt 3 } + \sqrt {{{\left( {2\sqrt 3 - 1} \right)}^2}} \\
= \sqrt {11 - 6\sqrt 3 } + 2\sqrt 3 - 1\\
e)\left( {\sqrt 3 + 4} \right)\sqrt {19 - 8\sqrt 3 } \\
= \left( {\sqrt 3 + 4} \right).\sqrt {{{\left( {4 - \sqrt 3 } \right)}^2}} \\
= \left( {\sqrt 3 + 4} \right).\left( {4 - \sqrt 3 } \right)\\
= {4^2} - 3\\
= 13\\
f)\sqrt {8 + 2\sqrt 7 } .\sqrt {\dfrac{{4 - \sqrt 7 }}{2}} \\
= \sqrt {{{\left( {\sqrt 7 + 1} \right)}^2}} .\sqrt {\dfrac{{8 - 2\sqrt 7 }}{4}} \\
= \left( {\sqrt 7 + 1} \right).\dfrac{{\sqrt {{{\left( {\sqrt 7 - 1} \right)}^2}} }}{2}\\
= \dfrac{1}{2}.\left( {\sqrt 7 + 1} \right)\left( {\sqrt 7 - 1} \right)\\
= \dfrac{1}{2}.\left( {7 - 1} \right)\\
= 3\\
g)\dfrac{{\sqrt 2 - \sqrt {11 + 6\sqrt 2 } }}{{\sqrt {6 + 2\sqrt 5 } - \sqrt 5 }}\\
= \dfrac{{\sqrt 2 - \sqrt {{{\left( {3 + \sqrt 2 } \right)}^2}} }}{{\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} - \sqrt 5 }}\\
= \dfrac{{\sqrt 2 - 3 - \sqrt 2 }}{{\sqrt 5 + 1 - \sqrt 5 }}\\
= - 3
\end{array}$
