Question

giúp mk giải phép toán này với ạ 

\(_{^{ }\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}}\)

Answer 1

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

\(=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)

\(=\left|\sqrt{2}+\sqrt{3}\right|-\left|\sqrt{2}-\sqrt{3}\right|\)

\(=\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{2}\)

\(=2\sqrt{2}\)