Question

\(\sqrt{11-2\sqrt{30}}-\sqrt{11+2\sqrt{30}}\)

Answer 1

Đặt \(A=\sqrt{11-2\sqrt{30}}-\sqrt{11+2\sqrt{30}}\)

\(\Leftrightarrow A^2=11-2\sqrt{30}+11+2\sqrt{30}-2\sqrt{\left(11-2\sqrt{30}\right)\left(11+2\sqrt{30}\right)}\)

\(\Leftrightarrow A^2=22-2\sqrt{11^2-\left(2\sqrt{30}\right)^2}\)

\(\Leftrightarrow A^2=22-2=20\)

\(\Leftrightarrow A=\pm\sqrt{20}\)

Answer 2

Vì \(\sqrt{11-2\sqrt{30}}< \sqrt{11+2\sqrt{30}}\)

Nên A chỉ nhận giá trị \(-\sqrt{20}\)