Đáp án+Giải thích các bước giải:

 `\sqrt{3\sqrt{3}+\sqrt{48-10\sqrt{7+4\sqrt{3}}}}`

`=\sqrt{3\sqrt{3}+\sqrt{48-10\sqrt{2^{2}+2.2.\sqrt{3}+(\sqrt{3})^{2}}}}`

`=\sqrt{3\sqrt{3}+\sqrt{48-10\sqrt{(2+\sqrt{3})^{2}}}}`

`=\sqrt{3\sqrt{3}+\sqrt{48-10.|2+\sqrt{3}|}}` 

`=\sqrt{3\sqrt{3}+\sqrt{48-10.(2+\sqrt{3})}}` (do `2+\sqrt{3}>0`)

`=\sqrt{3\sqrt{3}+\sqrt{48-20-10\sqrt{3}}}`

`=\sqrt{3\sqrt{3}+\sqrt{28-10\sqrt{3}}}`

`=\sqrt{3\sqrt{3}+\sqrt{5^{2}-2.5.\sqrt{3}+(\sqrt{3})^{2}}}`

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

`=\sqrt{3\sqrt{3}+|5-\sqrt{3}|}` 

`=\sqrt{3\sqrt{3}+5-\sqrt{3}}` (do `5-\sqrt{3}>0`)

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