Rationalize a Cube Root Binomial in Denominator

Learn how to rationalize a denominator containing a cube root binomial in this essential algebra tutorial! We'll tackle two detailed examples, showing you the step-by-step process to eliminate radicals from the denominator using the sum and difference of two cubes factoring formulas.

Rationalizing denominators is a crucial skill in algebra and precalculus, ensuring that expressions are in their simplest form. You'll understand the connection between these factoring identities and how they serve as the "conjugate" for cube root binomials, allowing you to transform complex denominators into simple integer values.

In this video, you'll learn:

A quick review of the sum of two cubes and difference of two cubes factoring formulas.
How to identify the 'a' and 'b' values in a cube root binomial denominator.
Constructing the trinomial "conjugate" needed to rationalize the denominator.
Applying the sum/difference of two cubes formulas to simplify the denominator.
Distributing terms in the numerator after rationalization.
Step-by-step solutions for two different cube root binomial rationalization problems.
Timestamps:

0:00 Introduction to Rationalizing Cube Root Binomials
0:20 Review: Sum of Two Cubes & Difference of Two Cubes Factoring
1:10 Example: Factoring x³ - 8 as a Difference of Two Cubes
2:10 Example 1: Rationalize 3 / (2 - ³√5)
3:00 Identifying 'a' and 'b' values for the Denominator
3:30 Constructing the Trinomial "Conjugate"
5:00 Multiplying the Numerator and Denominator by the Conjugate
5:30 Simplifying the Denominator using Difference of Two Cubes
6:20 Simplifying the Numerator and Final Answer
7:00 Example 2: Rationalize 5 / (3 + ³√2)
7:50 Identifying 'a' and 'b' values for the Denominator (Sum of Cubes)
8:10 Constructing the Trinomial "Conjugate" for Sum of Cubes
9:20 Simplifying the Denominator using Sum of Two Cubes
9:50 Distributing in the Numerator and Final Answer
10:50 Conclusion & More Resources
Master this advanced rationalization technique to excel in your algebra and precalculus courses! If you found this video helpful, please give it a thumbs up and subscribe to Mario's Math Tutoring for more math lessons!

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