Объяснение:

[tex]\sqrt{10-4\sqrt{6} } *(2+\sqrt{6})= \sqrt{6+4-4\sqrt{6} } *(2+\sqrt{6})=\\=\sqrt{(\sqrt{6})^2 -2*\sqrt{6} *2+2^2} *(2+\sqrt{6})=\sqrt{(\sqrt{6}-2)^2 } *(2+ \sqrt{6})=\\ = |\sqrt{6} -2|*(\sqrt{6}+2)= (\sqrt{6} -2)*(\sqrt{6}+2)=(\sqrt{6})^2-2^2=6-4=2.[/tex]