Đáp án:
$\begin{array}{l}
\sqrt {34 - 24\sqrt 2 } - 7 + 3\sqrt 2 \\
= \sqrt {34 - 2.12.\sqrt 2 } - 7 + 3\sqrt 2 \\
= \sqrt {18 - 2.3\sqrt 2 .4 + 16} - 7 + 3\sqrt 2 \\
= \sqrt {{{\left( {3\sqrt 2 - 4} \right)}^2}} - 7 + 3\sqrt 2 \\
= 3\sqrt 2 - 4 - 7 + 3\sqrt 2 \\
= 6\sqrt 2 - 11
\end{array}$