$a)\sqrt{5}\cdot \sqrt{45}=\sqrt{225}=15$  

$b)\sqrt{\frac{1}{{\sout{3}}^1}\cdot {\sout{48}}^{16}}=\sqrt{16}=4$  

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

$d)\sqrt[3]{\frac{1}{3}}\cdot \sqrt[3]{375}=\sqrt[3]{\frac{1}{{\sout{3}}^1}\cdot {\sout{375}}^{125}}=\sqrt[3]{125}=5$  

$e)\sqrt{6}\cdot \sqrt{10}\cdot \sqrt{15}=\sqrt{6\cdot 10\cdot 15}=\sqrt{900}=30$  

$f)\sqrt[3]{4}\cdot \sqrt[3]{10}\cdot \sqrt[3]{25}=\sqrt[3]{4\cdot 10\cdot 25}=\sqrt[3]{1000}=10$  

$g)\sqrt[3]{\frac{1}{2}}\cdot \sqrt[3]{\frac{2}{3}}\cdot \sqrt[3]{\frac{3}{8}}=\sqrt[3]{\frac{1}{{\sout{2}}^1}\cdot \frac{{\sout{2}}^1}{{\sout{3}}^1}\cdot \frac{{\sout{3}}^1}{8}}=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}$  

$h)\sqrt[3]{0,25}\cdot \sqrt[3]{\frac{1}{6}}\cdot \sqrt[3]{\frac{8}{9}}=\sqrt[3]{0,25\cdot \frac{1}{{\sout{6}}^3}\cdot \frac{{\sout{8}}^4}{9}}=\left(\frac{1}{{\sout{4}}^1}\cdot \frac{1}{3}\cdot \frac{{\sout{4}}^1}{9}\right)=\sqrt[3]{\frac{1}{27}}=\frac{1}{3}$