\frac{1}{\sqrt5-\sqrt2}=\frac{1(\sqrt5+\sqrt2)}{(\sqrt5-\sqrt2)(\sqrt5+\sqrt2)}=\frac{\sqrt5+\sqrt2}{5-2}=\frac{\sqrt5+\sqrt2}{3}
\frac{1}{\sqrt[3]7}=\frac{\sqrt[3]{7^2}}{\sqrt[3]7*\sqrt[3]{7^2}}=\frac{\sqrt[3]{14}}{\sqrt[3]{7^3}}=\frac{\sqrt[3]{14}}{7}