1)
[tex]2\sqrt{50}-4\sqrt8=2\sqrt{25\cdot2}-4\sqrt{4\cdot2}=\\\\=2\sqrt{5^2\cdot2}-4\sqrt{2^2\cdot2}=2\cdot5\sqrt2-4\cdot2\sqrt2=\\\\=10\sqrt2-8\sqrt2=\boxed{2\sqrt2}[/tex]
2)
[tex]\frac{\sqrt{50}-\sqrt{18}}{\sqrt2}=\frac{\sqrt{25\cdot2}-\sqrt{9\cdot2}}{\sqrt2}=\frac{\sqrt{5^2\cdot2}-\sqrt{3^2\cdot2}}{\sqrt2}=\frac{5\sqrt3-3\sqrt2}{\sqrt2}=\frac{2\sqrt2}{\sqrt2}=\boxed2\\[/tex]
3)
[tex]6\sqrt{20}:2\sqrt5=3\sqrt{20:5}=3\sqrt4=3\sqrt{2^2}=3\cdot2=\boxed6\\[/tex]
4)
[tex]\sqrt[3]{54}-3\sqrt[3]8=\sqrt[3]{27\cdot2}-3\sqrt[3]{2^3}=\\\\=\sqrt[3]{3^3\cdot2}-3\cdot2=3\sqrt[3]2-6=\boxed{3(\sqrt[3]2-2)}[/tex]
