Đáp án+Giải thích các bước giải:
2,
`\sqrt{(5+2\sqrt{2})^2}-\sqrt{(3-2\sqrt{2})^2}`
`=|5+2\sqrt{2}|-|3-2\sqrt{2}|`
`=5+2\sqrt{2}-(3-2\sqrt{2})`
`=5+2\sqrt{2}-3+2\sqrt{2}`
`=2+4\sqrt{2}`
3,
`\sqrt{(5-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}`
`=|5-2\sqrt{3}|+|3+2\sqrt{3}|`
`=5-2\sqrt{3}+3+2\sqrt{3}`
`=8`
4,
`\sqrt{(3+2\sqrt{6})^2}-\sqrt{(2-\sqrt{6})^2}`
`=|3+2\sqrt{6}|-|2-\sqrt{6}|`
`=3+2\sqrt{6}-(\sqrt{6}-2)`
`=3+2\sqrt{6}-\sqrt{6}+2`
`=5+\sqrt{6}`
5,
`\sqrt{(3+\sqrt{7})^2}+\sqrt{(5-2\sqrt{7})^2}`
`=|3+\sqrt{7}|+|5-2\sqrt{7}|`
`=3+\sqrt{7}+2\sqrt{7}-5`
`=3\sqrt{7}-2`
6,
`\sqrt{(4+\sqrt{15})^2}+\sqrt{(\sqrt{15}-3)^2}`
`=|4+\sqrt{15}|+|\sqrt{15}-3|`
`=4+\sqrt{15}+\sqrt{15}-3`
`=1+2\sqrt{15}`
7,
`\sqrt{(3-\sqrt{10})^2}-\sqrt{(\sqrt{10}-2)^2}`
`=|3-\sqrt{10}|-|\sqrt{10}-2|`
`=\sqrt{10}-3-(\sqrt{10}-2)`
`=\sqrt{10}-3-\sqrt{10}+2`
`=-1`
8,
`\sqrt{(2-\sqrt{3})^2}+\sqrt{(4-2\sqrt{3})^2}`
`=|2-\sqrt{3}|+|4-2\sqrt{3}|`
`=2-\sqrt{3}+4-2\sqrt{3}`
`=6-3\sqrt{3}`
9,
`\sqrt{(3-\sqrt{7})^2}-\sqrt{(2\sqrt{7}-6)^2}`
`=|3-\sqrt{7}|-|2\sqrt{7}-6|`
`=3-\sqrt{7}-(6-2\sqrt{7})`
`=3-\sqrt{7}-6+2\sqrt{7}`
`=-3+\sqrt{7}`
10,
`\sqrt{(2-\sqrt{5})^2}-\sqrt{(3\sqrt{5}-7)^2`
`=|2-\sqrt{5}|-|3\sqrt{5}-7|`
`=\sqrt{5}-2-(7-3\sqrt{5})`
`=\sqrt{5}-2-7+3\sqrt{5}`
`=4\sqrt{5}-9`
