Rationalize the denominator of \(\frac{\sqrt{15} - 3}{\sqrt{5} -\sqrt{3}}\)

Solution

• \(\frac{\sqrt{15} - 3}{\sqrt{5} -3}\) = \( (\frac{\sqrt{15}-3}{\sqrt{5}-\sqrt{3}})(\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}})\)


• = \( \frac{5\sqrt{3}-3\sqrt{3}-3\sqrt{5}+3\sqrt{5}}{5-3}\)


• = \( \frac{2\sqrt{3}}{2}\)


• = \( \sqrt{3}\)