Question

rút gọn ; N=\((6-2\sqrt{5}).(\sqrt{10}+\sqrt{2}).\sqrt{3+\sqrt{5}}\)

Answer 1

\(N=\left(6-2\sqrt{5}\right).\left(\sqrt{10}+\sqrt{2}\right).\sqrt{3+\sqrt{5}}\)

\(=\left(6-2\sqrt{5}\right).\sqrt{2}\left(\sqrt{5}+1\right).\sqrt{3+\sqrt{5}}\)

\(=\left(6-2\sqrt{5}\right).\left(\sqrt{5}+1\right).\sqrt{6+2\sqrt{5}}\)

=\(\left(6-2\sqrt{5}\right).\left(\sqrt{5}+1\right).\sqrt{\left(\sqrt{5}+1\right)^2}\)

\(=\left(6-2\sqrt{5}\right).\left(\sqrt{5}+1\right)^2\)

\(=\left(6-2\sqrt{5}\right).\left(6+2\sqrt{5}\right)=36-20=16\)