Đáp án:
$\begin{array}{l}
Lv3.1\\
A = \sqrt {4 + 2\sqrt 3 } = \sqrt {{{\left( {\sqrt 3 + 1} \right)}^2}} = \sqrt 3 + 1\\
B = \sqrt {7 + 4\sqrt 3 } = \sqrt {4 + 2.2.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} = 2 + \sqrt 3 \\
C = \sqrt {17 + 12\sqrt 2 } = \sqrt {9 + 2.3.2\sqrt 2 + 8} \\
= \sqrt {{{\left( {3 + 2\sqrt 2 } \right)}^2}} = 3 + 2\sqrt 2 \\
Lv3.2\\
A = \sqrt {4 - 2\sqrt 3 } = \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} = \sqrt 3 - 1\\
B = \sqrt {6 - 2\sqrt 5 } = \sqrt {5 - 2.\sqrt 5 + 1} = \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} = \sqrt 5 - 1\\
C = \sqrt {12 - 6\sqrt 3 } = \sqrt {9 - 2.3.\sqrt 3 + 3} \\
= \sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} = 3 - \sqrt 3 \\
Lv4:\\
A = \sqrt {4 - 2\sqrt 3 } - \sqrt 3 \\
= \sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} - \sqrt 3 \\
= \sqrt 3 - 1 - \sqrt 3 \\
= - 1\\
B = \sqrt {6 + 2\sqrt 5 } - \sqrt 5 \\
= \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} - \sqrt 5 \\
= \sqrt 5 + 1 - \sqrt 5 \\
= 1\\
C = \sqrt {17 - 12\sqrt 2 } + \sqrt 8 \\
= \sqrt {{{\left( {3 - 2\sqrt 2 } \right)}^2}} + 2\sqrt 2 \\
= 3 - 2\sqrt 2 + 2\sqrt 2 \\
= 3
\end{array}$
