Question

Tính: \(8\sqrt{2}\left(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\right)\)

Answer 1

\(8\sqrt{2}\left(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\right)\)

\(=8\sqrt{2}\left(\sqrt{16+2.4.\sqrt{8}+8}-\sqrt{16-2.4\sqrt{8}+8}\right)\)

\(=8\sqrt{2}\left(\sqrt{\left(4+\sqrt{8}\right)^2}-\sqrt{\left(4-\sqrt{8}\right)^2}\right)\)

\(=8\sqrt{2}\left(4+\sqrt{8}-4+\sqrt{8}\right)\)

\(=8\sqrt{2}.2\sqrt{8}\)

= 64

Answer 2

ta có\(8\sqrt{2}\cdot\left(\sqrt{24+16\sqrt{2}}-\sqrt{24-16\sqrt{2}}\right)=8\sqrt{2}\cdot\left(\sqrt{\left(4+\sqrt{8}\right)^2}-\sqrt{\left(4-\sqrt{8}\right)^2}\right)=8\sqrt{2}\cdot\left(4+\sqrt{8}-4+\sqrt{8}\right)=8\sqrt{2}\cdot2\sqrt{8}=64\)vây..................