# How to get a radical out of the denominator

## How to Rationalize a Radical Out of a Denominator Solving Radical Equations With Square Roots, Cube Roots, Two Radicals, Fractions, Rational Exponents

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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Simplifying square-root expressions: no variables. Simplifying square roots of fractions. Simplifying rational exponent expressions: mixed exponents and radicals. Simplifying square-root expressions: no variables advanced.

On the previous page, all the fractions containing radicals or radicals containing fractions had denominators that cancelled off or else simplified to whole numbers. What if we get an expression where the denominator insists on staying messy? This looks very similar to the previous exercise, but this is the "wrong" answer. Because the denominator contains a radical. The denominator must contain no radicals, or else it's "wrong". Why "wrong", in quotes?

By Yang Kuang, Elleyne Kase. Thus we do something called rationalizing the denominator. This convention makes collecting like terms easy, and your answers will be truly simplified. There are two separate situations where radicals may show up in the denominator of a fraction: where expressions contain one radical in the denominator, and where expressions contain two terms in the denominator, at least one of which is a radical. Rationalizing expressions with one radical in the denominator is easy. For example, with a square root, you just need to get rid of the square root. Normally, the best way to do that in an equation is to square both sides.

Rationalizing Denominators. Learning Objective s. Although radicals follow the same rules that integers do, it is often difficult to figure out the value of an expression containing radicals. These are much harder to visualize. That said, sometimes you have to work with expressions that contain many radicals. Often the value of these expressions is not immediately clear.

Radical fractions aren't little rebellious fractions that stay out late, drinking and smoking pot. Instead, they're fractions that include radicals — usually square roots when you're first introduced to the concept, but later on your might also encounter cube roots, fourth roots and the like, all of which are called radicals too. Depending on exactly what your teacher is asking you to do, there are two ways of simplifying radical fractions: Either factor the radical out entirely, simplify it, or "rationalize" the fraction, which means you eliminate the radical from the denominator but may still have a radical in the numerator. Consider your first option, factoring the radical out of the fraction. There are actually two ways of doing this.

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## Intro to rationalizing the denominator

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## 4 thoughts on “How to get a radical out of the denominator”

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Intro to rationalizing the denominator | Algebra (video) | Khan Academy

4. Vanessa T. says:

Rationalize one term numerators of rational expressions.