Rationalization of a Denominator

Method that can be used to convert the irrational denominator of certain fractional expressions into a rational number.

Consider the expression: [latex]\dfrac{1}{\sqrt{a}}[/latex] Therefore, we obtain: [latex]\dfrac{1}{\sqrt{a}}[/latex] × [latex]\dfrac{\sqrt{a}}{\sqrt{a}}[/latex] = [latex]\dfrac{\sqrt{a}}{a}[/latex] Consider the expression: [latex]\dfrac{1}{\sqrt{a} +\sqrt{b}}[/latex] Therefore, we obtain: [latex]\dfrac{1}{\sqrt{a} +\sqrt{b}}[/latex] × [latex]\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}[/latex] = [latex]\dfrac{\sqrt{a}-\sqrt{b}}{a-b}[/latex]

Examples

Consider the expression: [latex]\dfrac{36}{\sqrt{6}}[/latex] Therefore, we obtain: [latex]\dfrac{36}{\sqrt{6}}[/latex] × [latex]\dfrac{\sqrt{6}}{\sqrt{6}}[/latex] = [latex]\dfrac{36\sqrt{6}}{6}[/latex] = 6[latex]\sqrt{6}[/latex] Consider the expression: [latex]\dfrac{8}{\sqrt{7} +\sqrt{3}}[/latex] Therefore, we obtain: [latex]\dfrac{8}{\sqrt{7} +\sqrt{3}}[/latex] × [latex]\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}[/latex] = [latex]\dfrac{8(\sqrt{7}-\sqrt{3})}{4}[/latex] = [latex]2(\sqrt{7}-\sqrt{3})[/latex]

Rationalization of a Denominator

Examples

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