$\sqrt{0,5}=\sqrt{\frac{1}{2}}=\frac{\sqrt{1}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}=0,5\sqrt{2}$  

$\sqrt{4,5}=\sqrt{4\frac{1}{2}}=\sqrt{\frac{9}{2}}=\frac{\sqrt{9}}{\sqrt{2}}=\frac{3}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}}{2}=1,5\sqrt{2}$  

$\sqrt{2,88}=\sqrt{2\frac{22}{25}}=\sqrt{\frac{72}{25}}=\frac{\sqrt{72}}{\sqrt{25}}=\frac{\sqrt{9\cdot 8}}{5}=\frac{\sqrt{9}\cdot \sqrt{8}}{5}=\frac{3\cdot \sqrt{4\cdot 2}}{5}=$  

$=\frac{3\cdot \sqrt{4}\cdot \sqrt{2}}{5}=\frac{3\cdot 2\cdot \sqrt{2}}{5}=\frac{6\sqrt{2}}{5}=1,2\sqrt{2}$  

$\sqrt{3\frac{5}{9}}=\sqrt{\frac{32}{9}}=\frac{\sqrt{32}}{\sqrt{9}}=\frac{\sqrt{16\cdot 2}}{3}=\frac{\sqrt{16}\cdot \sqrt{2}}{3}=\frac{4\cdot \sqrt{2}}{3}=\frac{4\sqrt{2}}{3}=\frac{4}{3}\sqrt{2}$  

$\sqrt[3]{0,002}=\sqrt[3]{\frac{2}{1000}}=\frac{\sqrt[3]{2}}{\sqrt[3]{1000}}=\frac{\sqrt[3]{2}}{\sqrt[3]{{10}^3}}=\frac{\sqrt[3]{2}}{10}=0,1\sqrt[3]{2}$  

$\sqrt[3]{\frac{16}{27}}=\frac{\sqrt[3]{16}}{\sqrt[3]{27}}=\frac{\sqrt[3]{8\cdot 2}}{\sqrt[3]{3^3}}=\frac{\sqrt[3]{8}\cdot \sqrt[3]{2}}{3}=\frac{\sqrt[3]{2^3}\cdot \sqrt[3]{2}}{3}=\frac{2\cdot \sqrt[3]{2}}{3}=\frac{2\sqrt[3]{2}}{3}=\frac{2}{3}\sqrt[3]{2}$  

$\sqrt[3]{0,054}=\sqrt[3]{\frac{54}{1000}}=\frac{\sqrt[3]{54}}{\sqrt[3]{1000}}=\frac{\sqrt[3]{27\cdot 2}}{\sqrt[3]{{10}^3}}=\frac{\sqrt[3]{27}\cdot \sqrt[3]{2}}{10}=\frac{\sqrt[3]{3^3}\cdot \sqrt[3]{2}}{10}=\frac{3\cdot \sqrt[3]{2}}{10}=$  

$=\frac{3\sqrt[3]{2}}{10}=0,3\sqrt[3]{2}$  

$\sqrt[4]{0,0162}=\sqrt[4]{\frac{162}{10000}}=\frac{\sqrt[4]{162}}{\sqrt[4]{10000}}=\frac{\sqrt[4]{81\cdot 2}}{\sqrt[4]{{10}^4}}=\frac{\sqrt[4]{81}\cdot \sqrt[4]{2}}{10}=\frac{\sqrt[4]{3^4}\cdot \sqrt[4]{2}}{10}=\frac{3\cdot \sqrt[4]{2}}{10}=$  

$=\frac{3\sqrt[4]{2}}{10}=0,3\sqrt[4]{2}$