Đáp án:
`a.`
`\sqrt{3}+\sqrt{8-2\sqrt{15}}`
`=\sqrt{3}+\sqrt{5-2\sqrt{15}+3}`
`=\sqrt{3}+\sqrt{(\sqrt{5})^2-2.\sqrt{5}.\sqrt{3}+(\sqrt{3})^2}`
`=\sqrt{3}+\sqrt{(\sqrt{5}-\sqrt{3})^2}`
`=\sqrt{3}+|\sqrt{5}-\sqrt{3}|`
`=\sqrt{3}+\sqrt{5}-\sqrt{3}(Vì:\sqrt{5}>\sqrt{3})`
`=\sqrt{5}`
`b.`
`\sqrt{8+2\sqrt{7}}-\sqrt{7}`
`=\sqrt{7+2\sqrt{7}+1}-\sqrt{7}`
`=\sqrt{(\sqrt{7})^2+2.\sqrt{7}.1+1^2}-\sqrt{7}`
`=\sqrt{(\sqrt{7}+1)^2}-\sqrt{7}`
`=|\sqrt{7}+1|-\sqrt{7}`
`=\sqrt{7}+1-\sqrt{7}`
`=1`
`c.`
`\sqrt{22-2\sqrt{21}}-\sqrt{22+2\sqrt{21}}`
`=\sqrt{21-2\sqrt{21}+1}-\sqrt{21+2\sqrt{21}+1}`
`=\sqrt{(\sqrt{21})^2-2\sqrt{21}.1+1}-\sqrt{(\sqrt{21})^2+2.\sqrt{21}.1+1}`
`=\sqrt{(\sqrt{21}-1)^2}-\sqrt{(\sqrt{21}+1)^2}`
`=|\sqrt{21}-1|-|\sqrt{21}+1|`
`=\sqrt{21}-1-(\sqrt{21}+1)`
`=\sqrt{21}-1-\sqrt{21}-1`
`=-2`
`d.`
`\sqrt{7+4\sqrt{3}}-2\sqrt{3}`
`=\sqrt{4+4\sqrt{3}+3}-2\sqrt{3}`
`=\sqrt{2^2+2.2.\sqrt{3}+(\sqrt{3})^2}-2\sqrt{3}`
`=\sqrt{(2+\sqrt{3})^2}-2\sqrt{3}`
`=|2+\sqrt{3}|-2\sqrt{3}`
`=2+\sqrt{3}-2\sqrt{3}`
`=2-\sqrt{3}`
