Question

Rút Gọn Biểu Thức
D=\(\left(\sqrt{14}-\sqrt{6}\right)\left(5+\sqrt{21}\right)\sqrt{5-\sqrt{7}}\)

Answer 1

Sửa đề: \(D=\left(\sqrt{14}-\sqrt{6}\right)\cdot\left(5+\sqrt{21}\right)\cdot\sqrt{4-\sqrt{7}}\)

Ta có: \(D=\left(\sqrt{14}-\sqrt{6}\right)\cdot\left(5+\sqrt{21}\right)\cdot\sqrt{4-\sqrt{7}}\)

\(=\sqrt{2}\left(\sqrt{7}-\sqrt{3}\right)\cdot\left(5+\sqrt{21}\right)\cdot\sqrt{4-\sqrt{7}}\)

\(=\sqrt{8-2\sqrt{7}}\cdot\left(\sqrt{7}-\sqrt{3}\right)\cdot\left(5+\sqrt{21}\right)\)

\(=\left(\sqrt{7}-1\right)\cdot\left(\sqrt{7}-\sqrt{3}\right)\cdot\left(5+\sqrt{21}\right)\)

\(=\left(7-\sqrt{21}-\sqrt{7}+\sqrt{3}\right)\cdot\left(5+\sqrt{21}\right)\)

\(=35+7\sqrt{21}-5\sqrt{21}-21-5\sqrt{7}-7\sqrt{3}+5\sqrt{3}+3\sqrt{7}\)

\(=14+2\sqrt{21}-2\sqrt{7}-2\sqrt{3}\)