Đáp án:
Giải thích các bước giải:
`e)`
`(\sqrt{10+2\sqrt{21}})/(3+\sqrt{21})`
`=(\sqrt{7+2\sqrt{3}.\sqrt{7}+3})/[(\sqrt{3}+\sqrt{7})\sqrt{3}]`
`=(\sqrt{(\sqrt{3}+\sqrt{7})^2})/[(\sqrt{3}+\sqrt{7})\sqrt{3}]`
`=(\sqrt{3}+\sqrt{7})/[(\sqrt{3}+\sqrt{7})\sqrt{3}]`
`=(1)/[\sqrt{3}]`
`f)`
`(2\sqrt{8}-\sqrt{12} )/ (\sqrt{18} -\sqrt{48} )-(\sqrt{5}+\sqrt{27} )/ (\sqrt{30} +\sqrt{162} )`
`=(2\sqrt{8}-2\sqrt{3} )/ (\sqrt{6}.(\sqrt{3} -\sqrt{8}) )-(\sqrt{5}+\sqrt{27} )/ (\sqrt{6} (\sqrt{5}+\sqrt{27} ) )`
`=(2(\sqrt{8}-\sqrt{3} ))/ (\sqrt{6}.(\sqrt{3} -\sqrt{8}) )-(\sqrt{5}+\sqrt{27} )/ (\sqrt{6} (\sqrt{5}+\sqrt{27} ) )`
`=(-2(\sqrt{3}-\sqrt{8} ))/ (\sqrt{6}.(\sqrt{3} -\sqrt{8}) )-(\sqrt{5}+\sqrt{27} )/ (\sqrt{6} (\sqrt{5}+\sqrt{27} ) )`
`=(-2)/ (\sqrt{6} )-(1)/ (\sqrt{6} )`
`=(-3)/ \sqrt{6} `
`=- \sqrt{6} /2`
`g)`
`(3+2\sqrt{3} )/ (\sqrt{3} )+(2+\sqrt{2} )/ (\sqrt{2} +1 )-(\sqrt{2}+\sqrt{3})`
`=(2+\sqrt{3} )+((\sqrt{2}+1) \sqrt{2})/ (\sqrt{2} +1 )-(\sqrt{2}+\sqrt{3})`
`=2+\sqrt{3} + \sqrt{2}-\sqrt{2}-\sqrt{3}`
`=2`
