Đáp án+Giải thích các bước giải:

 `a)-\sqrt{0,1}.\sqrt{0,4}=-\sqrt{0,1.0,4}=-\sqrt{0,04}`

`=-\sqrt{(0,2)^{2}}=-0,2`

`b)(\sqrt{8}-3\sqrt{2}+\sqrt{10}).\sqrt{2}-\sqrt{5}`

`=\sqrt{2^{3}.2}-3\sqrt{2.2}+\sqrt{2^{2}.5}-\sqrt{5}`

`=\sqrt{16}-3\sqrt{2^{2}}+2\sqrt{5}-\sqrt{5}`

`=4-3.2+\sqrt{5}`

`=\sqrt{5}-2`

`c)\sqrt{17-\sqrt{33}}.\sqrt{17+\sqrt{33}}`

`=\sqrt{(17-\sqrt{33}).(17+\sqrt{33})}`

`=\sqrt{17^{2}-(\sqrt{33})^{2}}`

`=\sqrt{289-33}`

`=\sqrt{256}`

`=\sqrt{16^{2}}`

`=16`

`d)(3\sqrt{8}-\sqrt{18}+5\sqrt{2}+\sqrt[50}).3\sqrt{2}`

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

`=(3.2\sqrt{2}-3\sqrt{2}+5\sqrt{2}+5\sqrt{2}).3\sqrt{2}`

`=(6\sqrt{2}+7\sqrt{2}).3\sqrt{2}`

`=13\sqrt{2}.3\sqrt{2}`

`=39.\sqrt{2^{2}}`

`=39.2`

`=78`

`e)\sqrt{100}-\sqrt{32}.\sqrt{2}+\sqrt{18}.\sqrt{2}`

`=\sqrt{10^{2}}+\sqrt{2}.(\sqrt{3^{2}.2}-\sqrt{4^{2}.\sqrt{2})`

`=10+\sqrt{2}.(3\sqrt[2}-4\sqrt{2})`

`=10+\sqrt{2}.(-\sqrt{2})`

`=10-2`

`=8`

`f)(\sqrt{9/2}+\sqrt{(25)/(2)}-\sqrt{2}).\sqrt{2}`

`=(\sqrt{3^{2}}.\sqrt{2})/(\sqrt{2})+(\sqrt{5^{2}}.\sqrt{2})/(\sqrt{2})-\sqrt{2^{2}}`

`=3+5-2`

`=8-2`

`=6`

`g)2\sqrt{3}.(\sqrt{2}-3)+(\sqrt{2}-\sqrt{3})^{2}+6\sqrt{3}`

`=2\sqrt{6}-6\sqrt{3}+(\sqrt{2})^{2}-2.\sqrt{2}.\sqrt{3}+(\sqrt{3})^{2}+6\sqrt{3}`

`=2\sqrt{6}-2\sqrt{6}+2+3`

`=0+5`

`=5`