LESSON NOTES MENU
Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

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:

• 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, 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.