Đáp án:

 `2`

Giải thích các bước giải:

 `(4-\sqrt{15}).(\sqrt{10}+\sqrt{6}).\sqrt{4+\sqrt{15}}`

`=\sqrt{2}.(\sqrt{5}+\sqrt{3}).(4-\sqrt{15}).\sqrt{4+\sqrt{15}}`

`=(\sqrt{5}+\sqrt{3}).(4-\sqrt{15}).\sqrt{2.(4+\sqrt{15})}`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).\sqrt{8+2\sqrt{15}}`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).\sqrt{5+2\sqrt{15}+3}`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).\sqrt{(\sqrt{5})^{2}+2.\sqrt{5}.\sqrt{3}+(\sqrt{3})^{2}}`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).\sqrt{(\sqrt{5}+\sqrt{3})^{2}}`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).|\sqrt{5}+\sqrt{3}|`

`=(4-\sqrt{15}).(\sqrt{5}+\sqrt{3}).(\sqrt{5}+\sqrt{3})`

`=(4-\sqrt{15}).(8+2\sqrt{15})`

`=2.(4-\sqrt{15}).(4+\sqrt{15})`

`=2.[4^{2}-(\sqrt{15})^{2}]`

`=2.(16-15)`

`=2.1`

`=2`