Đặt $A = \sqrt{10,5+\sqrt{6}-4\sqrt{3}-4\sqrt{2}}-\sqrt{9,5-4\sqrt{3}}$
$\to A\sqrt2 = \sqrt{21+2\sqrt{6}-8\sqrt{3}-8\sqrt{2}}-\sqrt{19-8\sqrt{3}}$
$\to A\sqrt2 =\sqrt{4^2 + \left(\sqrt2\right)^2 + \left(\sqrt3\right)^2 + 2.\sqrt2.\sqrt3 - 2.4.\sqrt2 - 2.4.\sqrt3} - \sqrt{4^2 - 2.4.\sqrt3 + \left(\sqrt3\right)^2}$
$\to A\sqrt2 =\sqrt{\left(4 - \sqrt2 - \sqrt3\right)^2} - \sqrt{\left(4 - \sqrt3\right)^2}$
$\to A\sqrt2 = \left(4 - \sqrt2 - \sqrt3\right)- \left(4 - \sqrt3\right)$
$\to A\sqrt2 = -\sqrt2$
$\to A = -1$
