Đáp án: 2
Giải thích các bước giải:
\((2+\sqrt{3}).(\sqrt{6}-\sqrt{2}).(\sqrt{2-\sqrt{3}})=(2+\sqrt{3}).(\sqrt{3}-1)\sqrt{2}.\sqrt{2-\sqrt{3}}\)
\(=(2+\sqrt{3}).(\sqrt{3}-1).\sqrt{4-2\sqrt{3}}=(2+\sqrt{3}).(\sqrt{3}-1).\sqrt{(\sqrt{3}-1)^2}\)
\(=(2+\sqrt{3}).(\sqrt{3}-1).(\sqrt{3}-1)=(2+\sqrt{3})(\sqrt{3}-1)^2=(2+\sqrt{3})(4-2\sqrt{3})\)
\(=(2+\sqrt{3}).(2-\sqrt{3}).2=(2^2-\sqrt{3^2}).2=1.2=2\)