Đáp án:
$\begin{array}{l}
\sqrt {3 - 2\sqrt 2 } + \sqrt {3 + 2\sqrt 2 } \\
= \sqrt {2 - 2\sqrt 2 + 1} + \sqrt {2 + 2\sqrt 2 + 1} \\
= \sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} \\
= \sqrt 2 - 1 + \sqrt 2 + 1\\
= 2\sqrt 2 \\
\sqrt {7 + 2\sqrt 6 } - \sqrt {7 - 2\sqrt 6 } \\
= \sqrt {{{\left( {\sqrt 6 + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 6 - 1} \right)}^2}} \\
= \sqrt 6 + 1 - \left( {\sqrt 6 - 1} \right)\\
= 2\\
\sqrt {9 - 4\sqrt 5 } - \sqrt {{{\left( {2 + \sqrt 5 } \right)}^2}} \\
= \sqrt {{{\left( {\sqrt 5 - 2} \right)}^2}} - \left( {2 + \sqrt 5 } \right)\\
= \sqrt 5 - 2 - 2 - \sqrt 5 \\
= - 4\\
\sqrt {28 - 10\sqrt 3 } + \sqrt {13 - 4\sqrt 3 } \\
= \sqrt {25 - 2.5.\sqrt 3 + 3} + \sqrt {12 - 2.2\sqrt 3 + 1} \\
= \sqrt {{{\left( {5 - \sqrt 3 } \right)}^2}} + \sqrt {{{\left( {2\sqrt 3 - 1} \right)}^2}} \\
= 5 - \sqrt 3 + 2\sqrt 3 - 1\\
= 4 + \sqrt 3 \\
\sqrt {5 + 2\sqrt 6 } - \sqrt {{{\left( {\sqrt 3 - \sqrt 2 } \right)}^2}} \\
= \sqrt {{{\left( {\sqrt 3 + \sqrt 2 } \right)}^2}} - \left( {\sqrt 3 - \sqrt 2 } \right)\\
= \sqrt 3 + \sqrt 2 - \sqrt 3 + \sqrt 2 \\
= 2\sqrt 2
\end{array}$
