$a)$   $\sqrt{225\cdot 25}=\sqrt{225}\cdot \sqrt{25}=15\cdot 5=75$  

$b)$  

$\frac{\sqrt{242}}{\sqrt{72}}=\sqrt{\frac{242}{72}}=\sqrt{\frac{\sout{2}\cdot 121}{\sout{2}\cdot 36}}=\sqrt{\frac{121}{36}}=\frac{\sqrt{121}}{\sqrt{36}}=\frac{11}{6}=1\frac{5}{6}$  

 

$c)$   $\sqrt[3]{216\cdot 8}=\sqrt[3]{216}\cdot \sqrt[3]{8}=6\cdot 2=12$  

 

$d)$   $\frac{\sqrt[3]{250}}{\sqrt[3]{54}}=\sqrt[3]{\frac{250}{54}}=\sqrt[3]{\frac{\sout{2}\cdot 125}{\sout{2}\cdot 27}}=\sqrt[3]{\frac{125}{27}}=\frac{\sqrt[3]{125}}{\sqrt[3]{27}}=\frac{5}{3}=1\frac{2}{3}$