Đáp án:

 `2\sqrt{2}`

Giải thích các bước giải:

 `\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`

`=\sqrt{3+2\sqrt{6}+2}-\sqrt{3-2\sqrt{6}+2}`

`=\sqrt{(\sqrt{3})^{2}+2.\sqrt{3}.\sqrt{2}+(\sqrt{2})^{2}}-\sqrt{(\sqrt{3})^{2}-2.\sqrt{3}.\sqrt{2}+(\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})` (do `\sqrt{3}-\sqrt{2}>0`)

`=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}`

`=2\sqrt{2}`