$a)\sqrt{3}\cdot \sqrt{12}=\sqrt{3\cdot 12}=\sqrt{36}=6$  

$b)\sqrt{\frac{2}{3}\cdot \frac{3}{8}}=\sqrt{\frac{{\sout{2}}^1}{{\sout{3}}^1}\cdot \frac{{\sout{3}}^1}{{\sout{8}}^4}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$  

$c)\sqrt{1\frac{7}{25}}\cdot \sqrt{0,08}=\sqrt{1\frac{7}{25}\cdot 0,08}=\sqrt{\frac{32}{25}\cdot \frac{8}{100}}=\sqrt{\frac{32}{25}\cdot \frac{2}{25}}=\sqrt{\frac{64}{625}}=\frac{8}{25}$  

$d)\sqrt[3]{2}\cdot \sqrt[3]{32}=\sqrt[3]{2\cdot 32}=\sqrt[3]{64}=4$  

$e)\sqrt[3]{0,5}\cdot \sqrt[3]{54}=\sqrt[3]{0,5\cdot 54}=\sqrt[3]{27}=3$  

$f)\sqrt[3]{8,1}:\sqrt[3]{300}=\sqrt[3]{8,1:300}=\sqrt[3]{\frac{8,1}{300}}=\sqrt[3]{\frac{81}{3000}}=\sqrt[3]{\frac{27}{1000}}=\frac{3}{10}$  

$g)\sqrt{{34}^4}=\sqrt{{\left({34}^2\right)}^2}={34}^2=1156$  

$h)\sqrt[3]{{\left(-19\right)}^3}=-19$  

$i)\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$