Question

rút gọn:

\(A=\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)

Answer 1

ta có : \(A=\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)

\(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{8+2\sqrt{7}}\right)\)

\(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{\left(\sqrt{7}+1\right)^2}\right)\) \(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)^2=\left(4-\sqrt{7}\right)\left(8+2\sqrt{7}\right)\)

\(\Leftrightarrow A=2\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)=2\left(16-7\right)=2.9=18\)