Đáp án+Giải thích các bước giải:

 `c)C=(\sqrt{6-\sqrt{11}}+\sqrt{6+\sqrt{11}})^{2}`

`=(\sqrt{6-\sqrt{11}})^{2}+2.\sqrt{6-\sqrt{11}}.\sqrt{6+\sqrt[11}}+(\sqrt{6+\sqrt{11}})^{2}`

`=6-\sqrt{11}+6+\sqrt{11}+2\sqrt{6^{2}-(\sqrt{11})^{2}}`

`=12+2\sqrt{36-11}`

`=12+2\sqrt{25}`

`=12+2.5`

`=12+10`

`=22`

Vậy `C=22`

`d)D=\sqrt{11-4\sqrt{7}}=\sqrt{(\sqrt{7})^{2}-2.\sqrt{7}.2+2^{2}}`

`=\sqrt{(\sqrt{7}-2)^{2}}=|\sqrt{7}-2|=\sqrt{7}-2`

Vậy `D=\sqrt{7}-2`

`e)E=\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}`

`=\sqrt{2^{2}-2.2.\sqrt{2}+(\sqrt{2})^{2}}+\sqrt{(3\sqrt{2})^{2}-2.3\sqrt{2}.2+2^{2}}`

`=\sqrt{(2-\sqrt{2})^{2}}+\sqrt{(3\sqrt{2}-2)^{2}}`

`=|2-\sqrt{2}|+|3\sqrt{2}-2|`

`=2-\sqrt{2}+3\sqrt{2}-2`

`=2\sqrt{2}`

Vậy `E=2\sqrt{2}`

`k)K=\sqrt{20}-2\sqrt{45}-3\sqrt{80}+\sqrt{125}`

`=\sqrt{2^{2}.5}-2\sqrt{3^{2}.5}-3\sqrt{4^{2}.5}+\sqrt{5^{2}.5}`

`=2\sqrt{5}-2.3\sqrt{5}-3.4\sqrt{5}+5\sqrt{5}`

`=7\sqrt{5}-6\sqrt{5}-12\sqrt{5}`

`=-11\sqrt{5}`

vậy `K=-11\sqrt{5}`