Topic: Radical Expressions
Subtopic: Roots and Radicals
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:
- 10.1.1 Evaluate perfect roots algebraically
- 10.1.2 Approximate non-perfect roots electronically
- 10.1.3 Evaluate radical functions algebraically
- 10.1.4 Graph radical functions electronically
- 10.1.5 Find domain and range of radical functions
- 10.1.6 Find odd and even nth roots of xpower including knowing when absolute values are required on the answer
Terminology
Define: radical, radicand, index (of a radical), root, radical expression, radical function
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 10.1
- pg 661 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". Personally I appreciate that the Blitzer text sticks to the "principle" root. But just in case you run into it in other sources, the "two square roots of a number" means, e.g., 9 has two square roots 3 and -3 since either squared would make 9. Whereas 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 the bottom of page 661 and mid page 667 note that an 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".
- Examples 5 and 9 and the formula boxes that precede them discuss the need for absolute values. Pay special attention as to when you need the absolute value on the answer from a radical expression and when you don't. We will discuss this more in class.