Question

Thực hiện phép tính:  \(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

Answer 1

\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}=\sqrt{9+2.3.\sqrt{2}+2}-\sqrt{9-2.3.\sqrt{2}+2}\)

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

\(=2\sqrt{2}\)

Answer 2

\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

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

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

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