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Calculus IV
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Course: Algebra III / Intermediate Algebra
Topic: Radical Expressions
Subtopic: Roots and Radical Functions

Overview

This lesson covers radicals (square roots, cube roots, etc.) and radical functions (evaluating, graphs, domains). Soon we’ll start to work with radical expressions (adding, multiplying, FOILing, etc.) and radical equations (solving), so build a strong foundation of the basics now!

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: radical, radicand, index (of a radical), root, principle square root, radical expression, radical function

Text Notes

Note the definition of the "principle square root". Be aware that some text/websites will not only give the "principle" root but might discuss the "two square roots of a number". The "two square roots of a number" means, e.g., 9 has two square roots 3 and -3 since either squared would make 9. However, the "principle square root" occurs when the radical sign is already around the number and the answer is only positive, e.g., √9 = 3.

At this point in your text the author may state that an even root of a negative number is "not a Real number". Later in this chapter we will learn about "imaginary numbers" and then we will be able to get a result for the square root of a negative number such as √-9, but for now, you can just say that √-9 is a "non-Real number".

Pay special attention as to when you need the absolute value on the answer from a radical expression and when you don't, tricky! We will discuss this more in class.