Đáp án+Giải thích các bước giải:
$1)\sqrt2-\sqrt6\\=\sqrt2(1-\sqrt3)\\1<\sqrt3\\\to 1-\sqrt3<0\\\to (\sqrt2-1)(1-\sqrt3)<0\\\to \sqrt2(1-\sqrt3)-(1-\sqrt3)<0\\\to \sqrt2-\sqrt6<1-\sqrt3\\2)\sqrt{4+\sqrt7}-\sqrt{4-\sqrt7}-\sqrt2\\=\sqrt{\dfrac{8+2\sqrt7}{2}}-\sqrt{\dfrac{8-2\sqrt7}{2}}-\sqrt2\\=\sqrt{\dfrac{(\sqrt7+1)^2}{2}}-\sqrt{\dfrac{(\sqrt7-1)^2}{2}}-\sqrt2\\=\dfrac{\sqrt7+1}{\sqrt2}-\dfrac{\sqrt7-1}{\sqrt2}-\sqrt2\\=\dfrac{\sqrt7+1-\sqrt+1}{\sqrt2}-\sqrt2\\=\dfrac{2}{\sqrt2}-\sqrt2\\=\sqrt2-\sqrt2=0$
