\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)
\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16-2\cdot4\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)
\(=\sqrt{5}+1+4-\sqrt{5}\)( vì \(\sqrt{5}+1>0\)và \(4-\sqrt{5}>0\))
\(=5\)
\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)
\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16+8\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)
\(=\left|\sqrt{5}+1\right|+\left|4-\sqrt{5}\right|\)
\(=\sqrt{5}+1+4-\sqrt{5}\)
\(=5\)