Question

Rút gọn biểu thức sau:

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

Answer 1

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

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

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

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

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

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

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

\(=2\left(9-\left(\sqrt{5}\right)^2\right)\)

\(=2.4=8\)

Chỉ vậy thôi nha bạn ^_^

Answer 2

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

\(C=\sqrt{4}.\sqrt{6+2\sqrt{5}}\left(\sqrt{5}-1\right)\)

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

\(C=2.\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)=2.4=8\)