Question

rút gọn biểu thức sau:

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

Answer 1

\(\sqrt{11-6\sqrt{2}}-2\sqrt{2}=\sqrt{\left(3-\sqrt{2}\right)^2}-2\sqrt{2}\)

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

Answer 2

\(\sqrt{11-6\sqrt{2}}-2\sqrt{2}=\sqrt{11-2.3.\sqrt{2}}-2\sqrt{2}=\sqrt{\left(3-\sqrt{2}\right)^2}-2\sqrt{2}=\left|3-\sqrt{2}\right|-2\sqrt{2}=3-\sqrt{2}-2\sqrt{2}=3-3\sqrt{2}=3\left(1-\sqrt{2}\right)\)