Đáp án+Giải thích các bước giải:
`a)`
`\sqrt{11-4\sqrt{6}}`
`=\sqrt{8-4\sqrt{6}+3}`
`=\sqrt{(2\sqrt{2})^2-2.2\sqrt{2}.\sqrt{3}+(\sqrt{3})^2}`
`=\sqrt{(2\sqrt{2}-\sqrt{3})^2}`
`=|2\sqrt{2}-\sqrt{3}|`
`=2\sqrt{2}-\sqrt{3}(Vì:2\sqrt{2}>\sqrt{3})`
`b)`
`\sqrt{15+10\sqrt{2}}`
`=\sqrt{15+2.\sqrt{25.2}}`
`=\sqrt{15+2\sqrt{50}}`
`=\sqrt{10+2.\sqrt{10}.\sqrt{5}+5}`
`=\sqrt{(\sqrt{10}+\sqrt{5})^2}`
`=|\sqrt{10}+\sqrt{5}|`
`=\sqrt{10}+\sqrt{5}`
`c)`
`\sqrt{6-2\sqrt{5}}`
`=\sqrt{5-2\sqrt{5}+1}`
`=\sqrt{(\sqrt{5}-1)^2}`
`=|\sqrt{5}-1|`
`=\sqrt{5}-1(Vì:\sqrt{5}>1)`
`d)`
`\sqrt{11+4\sqrt{7}}`
`=\sqrt{7+4\sqrt{7}+4}`
`=\sqrt{(\sqrt{7})^2+2.2.\sqrt{7}+2^2}`
`=\sqrt{(\sqrt{7}+2)^2}`
`=|\sqrt{7}+2|`
`=\sqrt{7}+2`
