Question

Rút gọn:

a) \(A=\sqrt{4+2\sqrt{2}}\sqrt{2+2+\sqrt{2}}.\sqrt{2-2+\sqrt{2}}\)

b) \(B=\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)

c) \(C=\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6}+\sqrt{35}\right)\)

d) \(D=\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)

Answer 1

a, Nghe đề sai sai là lạ

b, Ta có : \(B=\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)

\(=\sqrt{4}-\sqrt{6+2\sqrt{5}}+2\sqrt{5}=2+2\sqrt{5}-\sqrt{5+2\sqrt{5}+1}\)

\(=2+2\sqrt{5}-\sqrt{5}-1=\sqrt{5}+1\)

c, Ta có : \(C=\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6}+\sqrt{35}\right)\)

\(=\sqrt{84}-\sqrt{60}+\sqrt{490}-\sqrt{350}=2\sqrt{21}-2\sqrt{15}+7\sqrt{10}-5\sqrt{14}\)

d, Ta có : \(D=\sqrt{11-4\sqrt{7}}-\sqrt{2}\sqrt{8+3\sqrt{7}}\)

\(=\sqrt{4-4\sqrt{7}+7}-\sqrt{9+6\sqrt{7}+7}\)

\(=\sqrt{7}-2-3-\sqrt{7}=-5\)