Đáp án + giải thích các bước giải:
a) `\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`
`=\sqrt{3+2.\sqrt{2}.\sqrt{3}+2}-\sqrt{3-2.\sqrt{2}.\sqrt{3}+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{2}`
b) `\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}`
`=\sqrt{9+2.3.\sqrt{2}+2}-\sqrt{9-2.3.\sqrt{2}+2}`
`=\sqrt{(3+\sqrt{2})^2}-\sqrt{(3-\sqrt{2})^2}`
`=|3+\sqrt{2}|-|3-\sqrt{2}|`
`=3+\sqrt{2}-3+\sqrt{2}`
`=2\sqrt{2}`