Simplifying Radical Expressions

Simplifying Radical Expressions

Author: Rachel Kaplan

In this learning packet, we will cover:
-Simplifying completely
-Rationalizing a denominator
-Using the product property of radicals
-Using the quotient property of radicals

Radicals (numbers with square roots on them) are often difficult to simplify. However, with this learning packet we will figure out everything you need to know about dealing with these tricky annoyances!

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What is a Radical?

Remember, a radical is simply a number with a square root, such as √4 ...which is the same as saying 41/2

Radical expressions are expressions with a radical as one or part of one of the terms. You will see many examples of these throughout the learning packet.

Another skill we will learn is how to rationalize a denominator. This involved making the denominator (bottom) of a fraction rational or, in other words, getting rid of the square root.



Simplifying Radicals

Rationalize the Denominator

Multiplying by the Conjugate Step by Step

How to multiply a fraction by the conjugate in order to rationalize it and remove the square root from the bottom. A step by step example problem.


Take a look at this awesome link if you need more practice. It provides all kinds of example problems and also includes step-by-step solutions if you get stuck:

Radical Problems