Question

\(\text{Rút gọn biểu thức :}\)

\(C=\sqrt{7+3\sqrt{5}}+\sqrt{3-\sqrt{5}}\)

Answer 1

\(C\sqrt{2}=\sqrt{14+6\sqrt{5}}+\sqrt{6-2\sqrt{5}}=\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

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

\(C=\sqrt{2}+\sqrt{10}\)