How to rationalize a denominator | Exponent expressions and equations | Algebra I | Khan Academy

TL;DR

Learn how to rationalize the denominator by multiplying the numerator and denominator by a conjugate or appropriate expression to simplify or eliminate square roots in the denominator.

Transcript

In this video, we're going to learn how to rationalize the denominator. What we mean by that is, let's say we have a fraction that has a non-rational denominator, the simplest one I can think of is 1 over the square root of 2. So to rationalize this denominator, we're going to just re-represent this number in some way that does not have an irration... Read More

Key Insights

• ❓ Rationalizing the denominator involves re-representing a fraction with an irrational denominator.
• 🤲 Rationalizing helps in getting numbers into a common format and for aesthetic reasons.
• 😑 Multiplying by an appropriate expression, such as a conjugate, can rationalize the denominator.
• 😒 Rationalizing binomial denominators may require the use of the difference of squares.

Questions & Answers

Q: Why do we rationalize denominators?

Rationalizing denominators is done to express numbers in a common format and for aesthetic purposes. It helps in computations and may have been preferred before calculators were widely available.

Q: How can we rationalize a fraction with a simple irrational denominator?

Multiply the numerator and denominator by the irrational number divided by itself. This allows us to re-represent the number without changing its value.

Q: Can we rationalize a binomial denominator?

No, the method used for a simple irrational denominator will not work for a binomial denominator with an irrational number. Instead, we can use the difference of squares to simplify and rationalize the denominator.

Q: Are there any advantages to rationalizing denominators with variables?

Rationalizing denominators with variables helps simplify expressions and eliminate square roots. It can make calculations easier and may be necessary in certain mathematical operations.

Summary & Key Takeaways

• Rationalizing the denominator involves re-representing a fraction with an irrational denominator to have a rational denominator.

• Rationalizing denominators helps to express numbers in a common format and for aesthetic reasons.

• Multiplying the numerator and denominator by an appropriate expression can rationalize the denominator.