Verified answer

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