Toán $\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}$ 06/07/2021 By Quinn $\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}$
`\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\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` Trả lời
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`. Trả lời
`\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`
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`.