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How to Rationalize Denominators

Fractions consist of a numerator on top and a denominator on bottom. Roots, or radicals, are the mathematical opposite of exponents, with the smallest radical being the square root, represented by the symbol √. The next highest root is the cube root, ³√. The small number in front of the radical sign is called the index number and it can be any whole number. When a radical appears in the denominator of a fraction, it can be removed through a process called rationalizing the denominator.

Instructions

- 1
  Rationalize the denominator of a fraction by first multiplying numerator and denominator by a square or cube that will cause the denominator to become a perfect square or perfect cube, which are numbers whose radical solution is a whole number. Simplify any remaining radicals, if possible, and simplify the fraction, if possible.
- 2
  Practice rationalizing the denominator with the rational expression 12 / √6. Note that this fraction can't be simplified at this time because the denominator is under a square root while the numerator isn't. Decide what to multiply the numerator and denominator by to get a perfect cube in the denominator: 12 * √6 / √6 * √6 = 12√6 / √36 = 12√6 / 6.
- 3
  Check whether the remaining radical of 12√6 / 6 can be simplified: because there are no perfect squares to pull out of 6, it can't be simplified further. Simplify the fraction by dividing 6 from the numbers not under a radical, making the final answer 2√6.

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