$a)\sqrt{8}=\sqrt{4\cdot 2}=\sqrt{4}\cdot \sqrt{2}=2\sqrt{2}$

$b)\sqrt{32}=\sqrt{16\cdot 2}=\sqrt{16}\cdot \sqrt{2}=4\sqrt{2}$

$c)\sqrt{75}=\sqrt{25\cdot 3}=\sqrt{25}\cdot \sqrt{3}=5\sqrt{3}$

$d)\sqrt{72}=\sqrt{36\cdot 2}=\sqrt{36}\cdot \sqrt{2}=6\sqrt{2}$

$e)\sqrt{98}=\sqrt{49\cdot 2}=\sqrt{49}\cdot \sqrt{2}=7\sqrt{2}$

$f)\sqrt{500}=\sqrt{100\cdot 5}=\sqrt{100}\cdot \sqrt{5}=10\sqrt{5}$

$g)\sqrt[3]{16}=\sqrt[3]{8\cdot 2}=\sqrt[3]{8}\cdot \sqrt[3]{2}=2\sqrt[3]{2}$

$h)\sqrt[3]{54}=\sqrt[3]{27\cdot 2}=\sqrt[3]{27}\cdot \sqrt[3]{2}=3\sqrt[3]{2}$

$i)\sqrt[3]{-250}=\sqrt[3]{2\cdot -125}=\sqrt[3]{2}\cdot \sqrt[3]{-125}=\sqrt[3]{2}\cdot \left(-5\right)=-5\sqrt[3]{2}$

$j)\sqrt[3]{-9000}=\sqrt[3]{-1000\cdot 9}=\sqrt[3]{-1000}\cdot \sqrt[3]{9}=-10\sqrt[3]{9}$