Question

1) \(\sqrt{4-\sqrt{15}}\) +\(\sqrt{5-\sqrt{21}}\)+\(\sqrt{6-\sqrt[]{35}}\)+\(\sqrt{6}\)

Giúp mình với ạ... Mình cảm ơn nhiều ạ :))

Answer 1

Đặt A=\(\sqrt{4-\sqrt{15}}+\sqrt{5-\sqrt{21}}+\sqrt{6-\sqrt{35}}+\sqrt{6}\)

=>A\(\sqrt{2}=\sqrt{8-2\sqrt{15}}+\sqrt{10-2\sqrt{21}}+\sqrt{12-2\sqrt{35}}+\sqrt{12}=\sqrt{5-2\sqrt{3.5}+3}+\sqrt{7-2\sqrt{3.7}+3}+\sqrt{7-2\sqrt{5.7}+5}+\sqrt{12}=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}+2\sqrt{3}=\sqrt{5}-\sqrt{3}+\sqrt{7}-\sqrt{3}+\sqrt{7}-\sqrt{5}+2\sqrt{3}=2\sqrt{7}-2\sqrt{3}+2\sqrt{3}=2\sqrt{7}\)

Answer 2

Bổ sung \(A\sqrt{2}=2\sqrt{7}\Rightarrow A=\sqrt{2}.\sqrt{7}=\sqrt{14}\)