It is important to know that rationalize means to multiply and divide by the same root.
(a)[tex]\frac{15}{8\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{15\sqrt[]{3}}{8\cdot3}=\frac{5\sqrt[]{3}}{8}[/tex](b)[tex]\frac{\sqrt[]{2}}{\sqrt[]{11}}\cdot\frac{\sqrt[]{11}}{\sqrt[]{11}}=\frac{\sqrt[]{2\cdot11}}{11}=\frac{\sqrt[]{22}}{11}[/tex](c)[tex]\frac{2\sqrt[]{10}}{3\sqrt[]{7}}\cdot\frac{\sqrt[]{7}}{\sqrt[]{7}}=\frac{2\sqrt[]{10\cdot7}}{3\cdot7}=\frac{2\sqrt[]{70}}{21}[/tex]
