Question

\(\sqrt[]{5+2\sqrt[]{6}}-\sqrt[]{5-2\sqrt{6}}\)

Answer 1

\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}=>\sqrt{5+2\sqrt{6}}=\sqrt{5-2\sqrt{6}}=>\left(\sqrt{5+2\sqrt{6}}\right)^2=\left(\sqrt{5-2\sqrt{6}}\right)^2=>5+2\sqrt{6}=5-2\sqrt{6}=>5+2\sqrt{6}-5+2\sqrt{6}=4\sqrt{6}\)

Answer 2

Xét (\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\))²= \(5+2\sqrt{6}+5-2\sqrt{6}-2\sqrt{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}\)=\(10-2\sqrt{25-24}\)=10-2=8

=> \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)=\(\sqrt{8}\)=\(2\sqrt{2}\) (Vì biểu thức có giá trị lớn hơn 0)