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 , which eliminates the radical from the bottom. For binomial denominators like , multiply by the conjugate to use the difference of squares pattern.
Showing a random 20 of 50 problems.
Example 1
mediumRationalize .
Example 2
challengeRationalize for , .
Example 3
mediumRationalize .
Example 4
mediumWhat is the conjugate of ?
Example 5
challengeRationalize (used in calculus derivative-of- derivation).
Example 6
easyRationalize .
Example 7
hardRationalize .
Example 8
mediumRationalize .
Example 9
mediumRationalize for .
Example 10
easyRationalize .
Example 11
easyRationalize .
Example 12
mediumRationalize .
Example 13
easyRationalize and simplify.
Example 14
challengeRationalize .
Example 15
mediumRationalize .
Example 16
mediumRationalize .
Example 17
mediumRationalize and simplify.
Example 18
easyRationalize .
Example 19
mediumRationalize .
Example 20
mediumRationalize .