Question

Rút gọn

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

Thực hiện phép tính

G=\(\sqrt[3]{2-\sqrt{5}}.\left(\sqrt[6]{9+4\sqrt{5}}+\sqrt[3]{2+\sqrt{5}}\right)\)

Answer 1

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

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

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

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

\(=5-1=6\)

Answer 2

\(G=\sqrt[3]{2-\sqrt{5}}\cdot\left(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2+\sqrt{5}}\right)\)

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