$\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}$

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1. `\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10(2+\sqrt{3})}}}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{(\sqrt{1})^2(\sqrt{3})^2-10\sqrt{3}+(\sqrt{25})^2}}}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{(5-1.\sqrt{3})^2}}}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+5(5-1.\sqrt{3})}}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+5(5-\sqrt{3})}`

   `= \sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}`

   `= \sqrt{4+\sqrt{25}}`

   `= \sqrt{4+5}`

   `= \sqrt{9}`

   `= 3`

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2. Đáp án:

   `\sqrt{4+\sqrt{5\sqrt3+5\sqrt{48-10\sqrt{7+4\sqrt3}}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{48-10\sqrt{4+2.2.\sqrt3+3}}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{48-10\sqrt{(2+\sqrt3)^2}}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{48-10(2+\sqrt3)}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{48-20-10\sqrt3}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{28-10\sqrt3}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{25-2.5.\sqrt3+3}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5\sqrt{(5-\sqrt3)^2}}}`

   `=\sqrt{4+\sqrt{5\sqrt3+5(5-\sqrt3)}}`

   `=\sqrt{4+\sqrt{5\sqrt3+25-5\sqrt3}}`

   `=\sqrt{4+\sqrt{25}}`

   `=\sqrt{4+5}`

   `=\sqrt{9}=3`.

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