Đáp án:
Giải thích các bước giải:
`(14/\sqrt{14}+(\sqrt{12}+\sqrt{30})/(\sqrt2+\sqrt5))\sqrt{5-\sqrt{21}}`
`= (\sqrt{14}+(2\sqrt{3}+\sqrt{30})/(\sqrt{2}+\sqrt5))\sqrt{5-\sqrt{21}}`
`= (\sqrt{14}+((2\sqrt3+\sqrt{30})(\sqrt{2}-\sqrt5))/((\sqrt2+\sqrt5)(\sqrt2-\sqrt5)))\sqrt{5-\sqrt{21}}`
`= (\sqrt{14} + (-3\sqrt6)/-3)\sqrt{5-\sqrt{21}}`
`= (\sqrt{14} + \sqrt6)\sqrt{5-\sqrt{21}}`
`(`Áp dụng : `a(b+c) = ab +ac)`
`= \sqrt{14}\sqrt{5-\sqrt{21}}+\sqrt6\sqrt{5-\sqrt{21}}`
`= \sqrt{14(5-\sqrt{21})} + \sqrt{6(5-\sqrt{21})}`
`= \sqrt{70-14\sqrt{21}} + \sqrt{30-6\sqrt{21}}`
`= \sqrt{(7-\sqrt{21})^2} + \sqrt{(3-\sqrt{21})^2}`
`= 7 - \sqrt{21} + \sqrt{21} - 3`
`= 7-3`
`= 4`
`->` đpcm
