Đáp án+Giải thích các bước giải:
`a)`
`\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}`
`=\sqrt{36-12\sqrt{5}+5}-\sqrt{36+12\sqrt{5}+5}`
`=\sqrt{6^2-2.6.\sqrt{5}+(\sqrt{5})^2}-\sqrt{6^2+2.6.\sqrt{5}+(\sqrt{5})^2}`
`=\sqrt{(6-\sqrt{5})^2}-\sqrt{(6+\sqrt{5})^2}`
`=|6-\sqrt{5}|-|6+\sqrt{5}|`
`=6-\sqrt{5}-6-\sqrt{5}(Vì:6>\sqrt{5})`
`=-2\sqrt{5}`
`b)`
`\sqrt{17+12\sqrt{2}}-\sqrt{17-12\sqrt{2}}`
`=\sqrt{9+12\sqrt{2}+8}-\sqrt{9-12\sqrt{2}+8}`
`=\sqrt{3^2+2.3.2\sqrt{2}+(2\sqrt{2})^2}-\sqrt{3^2-2.3.2\sqrt{2}+(2\sqrt{2})^2}`
`=\sqrt{(3+2\sqrt{2})^2}-\sqrt{(3-2\sqrt{2})^2}`
`=|3+2\sqrt{2}|-|3-2\sqrt{2}|`
`=3+2\sqrt{2}-3+2\sqrt{2}(Vì:3>\sqrt{2})`
`=4\sqrt{2}`
`c)`
`\sqrt{29-12\sqrt{5}}+\sqrt{29+12\sqrt{5}}`
`=\sqrt{20-12\sqrt{5}+9}+\sqrt{20+12\sqrt{5}+9}`
`=\sqrt{(2\sqrt{5})^2-2.3.2\sqrt{5}+3^2}+\sqrt{(2\sqrt{5})^2+2.3.2\sqrt{5}+3^2}`
`=\sqrt{(2\sqrt{5}-3)^2}+\sqrt{(2\sqrt{5}+3)^2}`
`=|2\sqrt{5}-3|+|2\sqrt{5}+3|`
`=2\sqrt{5}-3+2\sqrt{5}+3(Vì:2\sqrt{5}>3)`
`=4\sqrt{5}`
