Đặt \(A=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
\(\sqrt{2}A=\sqrt{8+2\sqrt{7}}-\sqrt{8-2\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}+1\right)^2}-\sqrt{\left(\sqrt{7}-1\right)^2}=\left|\sqrt{7}+1\right|-\left|\sqrt{7}-1\right|\)
\(=\sqrt{7}+1-\sqrt{7}+1=2\)\(\Rightarrow A=\sqrt{2}\)
\(\Rightarrow\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}=\sqrt{2}-\sqrt{2}=0\)