Radicals in Fractions - Rationalizing Denominators

Rationalize the denominators in the following fractions:

1.  $\dfrac{1}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{\sqrt{5}}{5}$
2. $\dfrac{2}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{2\sqrt{2}}{2}=\sqrt{2}$
3. $\dfrac{3}{2\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{3\sqrt{3}}{6}=\dfrac{\sqrt{3}}{2}$
4. $\dfrac{\sqrt{2}}{\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{\sqrt{6}}{3}$
5. $\dfrac{2\sqrt{3}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{2\sqrt{15}}{5}$
6. $\dfrac{3\sqrt{5}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{15}{5}=3$
7. $\dfrac{\sqrt{4}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{\sqrt{20}}{5}=\dfrac{2\sqrt{5}}{5}$
8. $\dfrac{2\sqrt{2}}{\sqrt{5}\sqrt{2}}=\dfrac{2}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{2\sqrt{5}}{5}$
9. $\dfrac{2}{\sqrt[3]{3}}\times \dfrac{\sqrt[3]{3}\sqrt[3]{3}}{\sqrt[3]{3}\sqrt[3]{3}} = \dfrac{2\sqrt[3]{3^2}}{3}=\dfrac{2\sqrt[3]{9}}{3}$
10. $\dfrac{1}{\sqrt[4]{2}}\times \dfrac{\sqrt[4]{2}\sqrt[4]{2}\sqrt[4]{2}}{\sqrt[4]{2}\sqrt[4]{2}\sqrt[4]{2}} = \dfrac{\sqrt[4]{2^3}}{2}=\dfrac{\sqrt[4]{8}}{2}$