Practice Rationalizing Denominators in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The process of eliminating radical expressions from the denominator of a fraction by multiplying the numerator and denominator by an appropriate expression (the radical itself or its conjugate).
A radical in the denominator is considered 'messy.' To clean it up, multiply top and bottom by the same radical (or conjugate). This works because \sqrt{a} \cdot \sqrt{a} = a, which eliminates the radical from the bottom. For binomial denominators like 3 + \sqrt{2}, multiply by the conjugate 3 - \sqrt{2} to use the difference of squares pattern.
Example 1
easyRationalize the denominator of \frac{5}{\sqrt{3}}.
Example 2
hardRationalize \frac{4}{3 + \sqrt{5}}.
Example 3
easyRationalize \frac{2}{\sqrt{7}}.
Example 4
mediumRationalize \frac{6}{\sqrt{2} - 1}.