Question

rút gọn

 

\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{192}\)

Answer 1

\(=2\sqrt{2\sqrt{3}}-10\sqrt{2\sqrt{3}}+32\sqrt{3}\)

\(=-8\sqrt{2\sqrt{3}}+32\sqrt{3}\)

Answer 2

\(\sqrt{8\sqrt{3}}=2\sqrt{2}\sqrt[4]{3}=2\sqrt[4]{4}.\sqrt[4]{3}=2\sqrt[4]{12}\)

\(2\sqrt{25\sqrt{12}}=10\sqrt{\sqrt{12}}=10\sqrt[4]{12}\)

\(4\sqrt{192}=4.8\sqrt{3}=32\sqrt{3}\)

Suy ra : \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{192}=2\sqrt[4]{12}-10\sqrt[4]{12}+32\sqrt{3}=-8\sqrt[4]{12}+32\sqrt{3}\)