`7) A = \sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}}`

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

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

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

`= 2\sqrt{5}`

Vậy `A = 2\sqrt{5}`

`8) (3 - \sqrt{2})\sqrt{11 + 6\sqrt{2}}`

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

`= (3 - \sqrt{2})|3 + \sqrt{2}|`

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

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

`= 9 - 2`

`= 7`

`9) \sqrt{22 + 12\sqrt{2}} - \sqrt{27 - 10\sqrt{2}}`

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

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

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

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

`= 4\sqrt{2} - 3`

`10) \sqrt{19 + 8\sqrt{3}} - \sqrt{13 - 4\sqrt{3}}`

`= \sqrt{(4 + \sqrt{3})^2} - \sqrt{(2\sqrt{3} - 1)^2}`

`= |4 + \sqrt{3}| - |2\sqrt{3} - 1|`

`= (4 + \sqrt{3}) - (2\sqrt{3} - 1)`

`= 4 + \sqrt{3} - 2\sqrt{3} + 1`

`= 5 - \sqrt{3}`

`11) \sqrt{51 - 10\sqrt{2}} - \sqrt{19 - 6\sqrt{2}}`

`= \sqrt{(5\sqrt{2} - 1)^2} - \sqrt{(3\sqrt{2} - 1)^2}`

`= |5\sqrt{2} - 1| - |3\sqrt{2} - 1|`

`= (5\sqrt{2} - 1) - (3\sqrt{2} - 1)`

`= 5\sqrt{2} - 1 - 3\sqrt{2} + 1`

`= 2\sqrt{2}`

`12) \sqrt{46 - 6\sqrt{5}} - \sqrt{9 + 4\sqrt{5}}`

`= \sqrt{(3\sqrt{5} - 1)^2} - \sqrt{(\sqrt{5} + 2)^2}`

`= |3\sqrt{5} - 1| - |\sqrt{5} + 2|`

`= (3\sqrt{5} - 1) - (\sqrt{5} + 2)`

`= 3\sqrt{5} - 1 - \sqrt{5} - 2`

`= 2\sqrt{5} - 3`