Đáp án + Giải thích các bước giải:
`a, \sqrt{7+2\sqrt{6}}-\sqrt{7-2\sqrt{6}}`
`=\sqrt{6+2\sqrt{6}.1+1}-\sqrt{6-2\sqrt{6}.1+1}`
`=\sqrt{(sqrt{6}+1)^2}-\sqrt{(sqrt{6}-1)^2}`
`=|\sqrt{6}+1|-|\sqrt{6}-1|`
`=\sqrt{6}+1-\sqrt{6}+1=2`
`b, \sqrt{9-2\sqrt{8}}-\sqrt{9+2\sqrt{8}}`
`=\sqrt{8-2\sqrt{8}.1+1}-\sqrt{8+2\sqrt{8}.1+1}`
`=\sqrt{(sqrt{8}-1)^2}-\sqrt{(sqrt{8}+1)^2}`
`=|\sqrt{8}-1|-|\sqrt{8}+1|`
`=\sqrt{8}-1-\sqrt{8}-1=-2`
`c, \sqrt{16-2\sqrt{15}}+\sqrt{16+2\sqrt{15}}`
`=\sqrt{15-2\sqrt{15}.1+1}+\sqrt{15+2\sqrt{15}.1+1}`
`=\sqrt{(sqrt{15}-1)^2}+\sqrt{(sqrt{15}+1)^2}`
`=|\sqrt{15}-1|+|\sqrt{15}+1|`
`=\sqrt{15}-1+\sqrt{15}+1=2\sqrt{15}`
`d, \sqrt{6-4\sqrt{2}}+\sqrt{9-4\sqrt{2}}`
`=\sqrt{4-2.2\sqrt{2}+2}+\sqrt{(2\sqrt{2})^2+2.2\sqrt{2}.1+1}`
`=\sqrt{(sqrt{4}-\sqrt{2})^2}+\sqrt{(2\sqrt{2}+1)^2}`
`=|sqrt{4}-\sqrt{2}|+|2\sqrt{2}+1|`
`=2-\sqrt{2}+2\sqrt{2}+1=3+\sqrt{2}`
`e, \sqrt{14+6\sqrt{5}}-\sqrt{14-6\sqrt{5}}`
`=\sqrt{9+2.3.\sqrt{5}+5}-\sqrt{9-2.3.\sqrt{5}+5}`
`=\sqrt{(3+sqrt{5})^2}-\sqrt{(3-sqrt{5})^2}`
`=|3+sqrt{5}|-|3-sqrt{5}|`
`=3+sqrt{5}-3+sqrt{5}=2\sqrt{5}`
