Đặt \(A=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}-\sqrt{2}\)
Đặt \(B=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\)
\(\Leftrightarrow B^2=2-\sqrt{3}-2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+2+\sqrt{3}\)
\(\Leftrightarrow B^2=4-2\sqrt{4-3}\)
\(\Leftrightarrow B^2=4-2\)
\(\Leftrightarrow B^2=2\)
Vì \(B< 0\Rightarrow B=-\sqrt{2}\)
\(\Rightarrow A=-\sqrt{2}-\sqrt{2}=-2\sqrt{2}\)