Đáp án:
`2+\sqrt{3}-\sqrt{2}`
Giải thích các bước giải:
`(\sqrt{\sqrt{7+\sqrt{48}}}-\sqrt{\sqrt{28-16\sqrt{3}}}).\sqrt{\sqrt{7+\sqrt{48}}}`
`=\sqrt{\sqrt{7+\sqrt{48}}}.\sqrt{\sqrt{7+\sqrt{48}}}-\sqrt{\sqrt{28-16\sqrt{3}}}.\sqrt{\sqrt{7+\sqrt{48}}}`
`=\sqrt{7+\sqrt{48}}-\sqrt{\sqrt{2^2 . (7-4\sqrt{3})}}.\sqrt{\sqrt{7+\sqrt{4^2 .3}}}`
`=\sqrt{7+\sqrt{4^2 . 3}}-\sqrt{2\sqrt{7-4\sqrt{3}}}.\sqrt{\sqrt{7+4\sqrt{3}}}`
`=\sqrt{7+4\sqrt{3}}-\sqrt{2\sqrt{7-4\sqrt{3}}.\sqrt{7+4\sqrt{3}}}`
`=\sqrt{2^2+2.2.\sqrt{3}+3}-\sqrt{2.\sqrt{(7-4\sqrt{3}).(7+4\sqrt{3})}}`
`=\sqrt{(2+\sqrt{3})^2}-\sqrt{2.\sqrt{7^2-(4\sqrt{3})^2}}`
`=|2+\sqrt{3}|-\sqrt{2.\sqrt{49-48}}`
`=2+\sqrt{3}-\sqrt{2}`
Vậy: `(\sqrt{\sqrt{7+\sqrt{48}}}-\sqrt{\sqrt{28-16\sqrt{3}}}).\sqrt{\sqrt{7+\sqrt{48}}}=2+\sqrt{3}-\sqrt{2}`
