Question

Rút gọn \(\sqrt{6+2.\sqrt{5}}+\sqrt{21-8.\sqrt{5}}\) 

Answer 1

\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)

\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16-2\cdot4\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)

\(=\sqrt{5}+1+4-\sqrt{5}\)( vì \(\sqrt{5}+1>0\)và \(4-\sqrt{5}>0\))

\(=5\)

Answer 2

\(\sqrt{6+2\sqrt{5}}+\sqrt{21-8\sqrt{5}}\)

\(=\sqrt{5+2\sqrt{5}+1}+\sqrt{16+8\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(4-\sqrt{5}\right)^2}\)

\(=\left|\sqrt{5}+1\right|+\left|4-\sqrt{5}\right|\)

\(=\sqrt{5}+1+4-\sqrt{5}\)

\(=5\)