4.
[tex]\sqrt[3]{2\sqrt{2}}\cdot2^{\frac{1}{2}} = \sqrt[3]{\sqrt{2^{2}\cdot2}}}\cdot2^{\frac{1}{2}} =\sqrt[3]{\sqrt{2^{3}}}\cdot2^{\frac{1}{2}} = ((2^{3})^{\frac{1}{2}})^{\frac{1}{3}}\cdot2^{\frac{1}{2}} = 2^{3\cdot\frac{1}{2}\cdot\frac{1}{3}}\cdot2^{\frac{1}{2}} =\\\\=2^{\frac{1}{2}}\cdot2^{\frac{1}{2}} = 2^{\frac{1}{2}+\frac{1}{2}} = 2^{1} = 2 \ \ \in Q\\\\c.n.u.[/tex]
