Đáp án:
$a,2\sqrt{3}$
$b,22$
Giải thích các bước giải:
$\begin{array}{l}a,\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}}\\=\sqrt{3+2\sqrt{3}.\sqrt{2}+2}+\sqrt{3-2\sqrt{3}.\sqrt{2}+2}\\=\sqrt{(\sqrt{3}+\sqrt{2})^2}+\sqrt{(\sqrt{3}-\sqrt{2})^2}\\=|\sqrt{3}+\sqrt{2}|+|\sqrt{3}-\sqrt{2}|\\=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}\\=2\sqrt{3}\\b,\sqrt{(11-6\sqrt{2})^2}+\sqrt{(11+6\sqrt{2})^2}\\=|11-6\sqrt{2}|+|11+6\sqrt{2}|\\=11-6\sqrt{2}+11+6\sqrt{2}\\=22.\end{array}$