Ta có: \(\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{3-2\sqrt{2}}}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{2-2\sqrt{2}\cdot1+1}}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{\left(\sqrt{2}-1\right)^2}}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\left|\sqrt{2}-1\right|}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\left(\sqrt{2}-1\right)}}\)(Vì \(\sqrt{2}>1\))
\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{2}+8}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{18-8\sqrt{2}}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{16-2\cdot4\cdot\sqrt{2}+2}}\)
\(=\sqrt{4\sqrt{2}+4\sqrt{\left(4-\sqrt{2}\right)^2}}\)
\(=\sqrt{4\sqrt{2}+4\left|4-\sqrt{2}\right|}\)
\(=\sqrt{4\sqrt{2}+4\left(4-\sqrt{2}\right)}\)(Vì \(4>\sqrt{2}\))
\(=\sqrt{4\sqrt{2}+16-4\sqrt{2}}\)
\(=\sqrt{16}=4\)
