Rationalizing Denominators and Numerators of Radical Expressions
To eliminate radicals from the denominator of a fraction, you can use a method for simplifying radical expressions called rationalizing the denominator.
This process is also called "rationalizing the denominator" since we remove all irrational numbers in the denominator of the fraction.
Reminder: From earlier algebra, you will recall the difference of squares formula: (a + b)(a − b) = a2 − b2
We will use this formula to rationalize denominators.
Rationalizing the denominator means to get rid of any radicals in the denominator. To rationalize a denominator containing more than one term:
Step 1: Find the conjugate of the denominator.
Step 2: Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1. Step 3: Make sure all radicals are simplified.
Step 4: Simplify the fraction if needed.
Find out more about simplifying radical expressions below.
Practice: Answer the exercise below about rationalizing denominators and numerators of radical expressions.
Rationalizing Denominators and Numerators of Radical Expressions 1