Đáp án:
`1.`
`\sqrt{5+2\sqrt{6}}-\sqrt{3}`
`=\sqrt{3+2\sqrt{6}+2}-\sqrt{3}`
`=\sqrt{(\sqrt{3})^2+2.\sqrt{3}.\sqrt{2}+(\sqrt{2})^2}-\sqrt{3}`
`=\sqrt{(\sqrt{3}+\sqrt{2})^2}-\sqrt{3}`
`=|\sqrt{3}+\sqrt{2}|-\sqrt{3}`
`=\sqrt{3}+\sqrt{2}-\sqrt{3}`
`=\sqrt{2}`
`2.`
`\sqrt{7+2\sqrt{10}}-\sqrt{7-2\sqrt{10}}`
`=\sqrt{5+2\sqrt{10}+2}-\sqrt{5-2\sqrt{10}+2}`
`=\sqrt{(\sqrt{5})^2+2.\sqrt{5}.\sqrt{2}+(\sqrt{2})^2}-\sqrt{(\sqrt{5})^2-2.\sqrt{5}.\sqrt{2}+(\sqrt{2})^2}`
`=\sqrt{(\sqrt{5}+\sqrt{2})^2}-\sqrt{(\sqrt{5}-\sqrt{2})^2}`
`=|\sqrt{5}+\sqrt{2}|-|\sqrt{5}-\sqrt{2}|`
`=\sqrt{5}+\sqrt{2}-(\sqrt{5}-\sqrt{2})`
`=\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}`
`=2\sqrt{2}`
`3.`
`\sqrt{9-2\sqrt{14}}-\sqrt{9+2\sqrt{14}}`
`=\sqrt{7-2\sqrt{14}+2}-\sqrt{7+2\sqrt{14}+2}`
`=\sqrt{(\sqrt{7})^2-2.\sqrt{7}.\sqrt{2}+(\sqrt{2})^2}-\sqrt{(\sqrt{7})^2+2.\sqrt{7}.\sqrt{2}+(\sqrt{2})^2}`
`=\sqrt{(\sqrt{7}-\sqrt{2})^2}-\sqrt{(\sqrt{7}+\sqrt{2})^2}`
`=|\sqrt{7}-\sqrt{2}|-|\sqrt{7}+\sqrt{2}|`
`=\sqrt{7}-\sqrt{2}-(\sqrt{7}+\sqrt{2})`
`=\sqrt{7}-\sqrt{2}-\sqrt{7}-\sqrt{2}`
`=-2\sqrt{2}`
