a/ $\sqrt{6-2\sqrt 5}-\sqrt{6+2\sqrt 5}\\=\sqrt{5-2\sqrt 5+1}-\sqrt{5+2\sqrt 5+1}\\=\sqrt{(\sqrt 5)^2-2\sqrt 5.1+1^2}-\sqrt{(\sqrt 5)^2+2\sqrt 5.1+1^2}\\=\sqrt{(\sqrt 5-1)^2}-\sqrt{(\sqrt 5+1)^2}\\=|\sqrt 5-1|-|\sqrt 5+1|\\=(\sqrt 5-1)-(\sqrt 5+1)(vì\,\,\sqrt 5-1>0,\sqrt 5+1>0)\\=\sqrt 5-1-\sqrt 5-1\\=-2$
Vậy $\sqrt{6-2\sqrt 5}-\sqrt{6+2\sqrt 5}=-2$
b/ $\sqrt{3+2\sqrt 2}-\sqrt{8-2\sqrt 7}\\=\sqrt{2+2\sqrt 2+1}-\sqrt{7-2\sqrt 7+1}\\=\sqrt{(\sqrt 2)^2+2\sqrt 2.1+1^2}-\sqrt{(\sqrt 7)^2-2\sqrt 7.1+1^2}\\=\sqrt{(\sqrt 2+1)^2}-\sqrt{(\sqrt 7-1)^2}\\=|\sqrt 2+1|-|\sqrt 7-1|\\=(\sqrt 2+1)-(\sqrt 7-1)(vì\,\,\sqrt 2+1>0,\sqrt 7-1>0)\\=\sqrt 2+1-\sqrt 7+1\\=-\sqrt 7+2+\sqrt 2$
Vậy $\sqrt{3+2\sqrt 2}-\sqrt{8-2\sqrt 7}=-\sqrt 7+2+\sqrt 2$
c/ $(3-\sqrt 2).\sqrt{11+6\sqrt 2}\\=(3-\sqrt 2).\sqrt{9+6\sqrt 2+2}\\=(3-\sqrt 2).\sqrt{3^2+2.3.\sqrt 2+(\sqrt 2)^2}\\=(3-\sqrt 2).\sqrt{(3+\sqrt 2)^2}\\=(3-\sqrt 2).|3+\sqrt 2|\\=(3-\sqrt 2)(3+\sqrt 2)(vì\,\,3+\sqrt 2>0)\\=3^2-(\sqrt 2)^2\\=9-2\\=7$
Vậy $(3-\sqrt 2).\sqrt{11+6\sqrt 2}=7$
d/ $(\sqrt{10}+2\sqrt 5)\sqrt{6-4\sqrt 2}\\=(\sqrt{5.2}+2\sqrt 5).\sqrt{4-4\sqrt 2+2}\\=\sqrt 5(\sqrt 2+2).\sqrt{2^2-2.2.\sqrt 2+(\sqrt 2)^2}\\=\sqrt 5(\sqrt 2+2).\sqrt{(2-\sqrt 2)^2}\\=\sqrt 5.(\sqrt 2+2).|2-\sqrt 2|\\=\sqrt 5.(\sqrt 2+2).(2-\sqrt 2)(vì\,\,2-\sqrt 2>0)\\=\sqrt 5[2^2-(\sqrt 2)^2]\\=\sqrt{5}.(4-2)\\=2\sqrt 5$
Vậy $(\sqrt{10}+2\sqrt 5)\sqrt{6-4\sqrt 2}=2\sqrt 5$
