`1)` `\sqrt{5 + 2\sqrt{6}}`

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

`= \sqrt{(\sqrt{3})^2 + 2.\sqrt{3}.\sqrt{2} + (\sqrt{2})^2}`

`= \sqrt{(\sqrt{3} + \sqrt{2})^2}`

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

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

`2)` `\sqrt{14 - 2\sqrt{33}}`

`= \sqrt{11 - 2\sqrt{33} + 3}`

`= \sqrt{(\sqrt{11})^2 - 2.\sqrt{11}.\sqrt{3} + (\sqrt{3})^2}`

`= \sqrt{(\sqrt{11} - \sqrt{3})^2}`

`= |\sqrt{11} - \sqrt{3}|`

`= \sqrt{11} - \sqrt{3}`

`3)` `\sqrt{18 - 2\sqrt{65}}`

`= \sqrt{13 - 2\sqrt{65} + 5}`

`= \sqrt{(\sqrt{13})^2 - 2.\sqrt{13}.\sqrt{5} + (\sqrt{5})^2}`

`= \sqrt{(\sqrt{13} - \sqrt{5})^2}`

`= |\sqrt{13} - \sqrt{5}|`

`= \sqrt{13} - \sqrt{5}`

`4)` `\sqrt{27 + 10\sqrt{2}}`

`= \sqrt{25 + 2.5.\sqrt{2} + 2}`

`= \sqrt{5^2 + 2.5.\sqrt{2} + (\sqrt{2})^2}`

`= \sqrt{(5 + \sqrt{2})^2}`

`= |5 + \sqrt{2}|`

`= 5 + \sqrt{2}`

`--------` Bonus nếu cần check:

`5)` `\sqrt{23 + 4\sqrt{15}}`

`= \sqrt{20 + 2.\sqrt{20}.\sqrt{3} + 3}`

`= \sqrt{(\sqrt{20})^2 + 2.\sqrt{20}.\sqrt{3} + (\sqrt{3})^2}`

`= \sqrt{(\sqrt{20} + \sqrt{3})^2}`

`= |\sqrt{20} + \sqrt{3}|`

`= 2\sqrt{5} + \sqrt{3}`

`6)` `\sqrt{16 - 2\sqrt{55}}`

`= \sqrt{11 - 2\sqrt{55} + 5}`

`= \sqrt{(\sqrt{11})^2 - 2.\sqrt{11}.\sqrt{5} + (\sqrt{5})^2}`

`= \sqrt{(\sqrt{11} - \sqrt{5})^2}`

`= |\sqrt{11} - \sqrt{5}|`

`= \sqrt{11} - \sqrt{5}`

`7)` `\sqrt{8 - 2\sqrt{12}}`

`= \sqrt{6 - 2\sqrt{12} + 2}`

`= \sqrt{(\sqrt{6})^2 - 2.\sqrt{6}.\sqrt{2} + (\sqrt{2})^2}`

`= \sqrt{(\sqrt{6} - \sqrt{2})^2}`

`= |\sqrt{6} - \sqrt{2}|`

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

`8)` `\sqrt{8 + 2\sqrt{15}}`

`= \sqrt{5 + 2\sqrt{15} + 3}`

`= \sqrt{(\sqrt{5})^2 + 2.\sqrt{5}.\sqrt{3} + (\sqrt{3})^2}`

`= \sqrt{(\sqrt{5} + \sqrt{3})^2}`

`= |\sqrt{5} + \sqrt{3}|`

`= \sqrt{5} + \sqrt{3}`

$\color{#FF0000}{♡^♡}\color{#FF7F00}{𝖘}\color{#FFD700}{𝖒}\color{#00FF00}{𝖕}\color{#00BFFF}{9}\color{#0000FF}{9}\color{#9400D3}{9}\color{#FF0000}{♡^♡}$