Question

Rút gọc các biểu thức:

a) 2\(\sqrt{40\sqrt{12}}\)-2\(\sqrt{\sqrt{75}}\)-3\(\sqrt{5\sqrt{48}}\)

b) 2\(\sqrt{8\sqrt{3}}\)-2\(\sqrt{5\sqrt{3}}\)-3\(\sqrt{20\sqrt{3}}\)

Answer 1

a: \(=2\sqrt{\sqrt{3}}\cdot4\sqrt{5}-2\cdot\sqrt{\sqrt{3}}\cdot\sqrt{5}-3\cdot\sqrt{\sqrt{3}}\cdot2\sqrt{5}\)

\(=2\sqrt{\sqrt{3}}\left(4\sqrt{5}-\sqrt{5}-3\sqrt{5}\right)=0\)

b: \(=2\cdot2\sqrt{2}\cdot\sqrt{\sqrt{3}}-2\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}-3\cdot2\sqrt{5}\cdot\sqrt{\sqrt{3}}\)

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