Method that can be used to convert the irrational denominator of certain fractional expressions into a rational number.
Consider the expression: \(\dfrac{1}{\sqrt{a}}\)
Therefore, we obtain: \(\dfrac{1}{\sqrt{a}}\) × \(\dfrac{\sqrt{a}}{\sqrt{a}}\) = \(\dfrac{\sqrt{a}}{a}\)
Therefore, we obtain: \(\dfrac{1}{\sqrt{a}}\) × \(\dfrac{\sqrt{a}}{\sqrt{a}}\) = \(\dfrac{\sqrt{a}}{a}\)
Consider the expression: \(\dfrac{1}{\sqrt{a} +\sqrt{b}}\)
Therefore, we obtain: \(\dfrac{1}{\sqrt{a} +\sqrt{b}}\) × \(\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}\) = \(\dfrac{\sqrt{a}-\sqrt{b}}{a-b}\)
Examples
Consider the expression: \(\dfrac{36}{\sqrt{6}}\)
Therefore, we obtain: \(\dfrac{36}{\sqrt{6}}\) × \(\dfrac{\sqrt{6}}{\sqrt{6}}\) = \(\dfrac{36\sqrt{6}}{6}\) = 6\(\sqrt{6}\)
Consider the expression: \(\dfrac{8}{\sqrt{7} +\sqrt{3}}\)
Therefore, we obtain: \(\dfrac{8}{\sqrt{7} +\sqrt{3}}\) × \(\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}\) = \(\dfrac{8(\sqrt{7}-\sqrt{3})}{4}\) = \(2(\sqrt{7}-\sqrt{3})\)