Question

rút gọn: A=\(\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)

Answer 1

\(A=\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)

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

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

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

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

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

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

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

\(=2\left(9-5\right)=8\)