# Ch 9: Radical Expressions & Functions

### About This Chapter

## Radical Expressions & Functions - Chapter Summary

How do you solve radical equations? Simplify radical expressions? Graph radical functions? The short lessons you'll find in this chapter provide detailed explanations and step-by-step summaries of how to work with radical expressions and functions. Each chapter is taught by an expert instructor, and the material is discussed in easy-to-follow terms. Every lesson is accessible 24/7 from any device, which means you can review these math concepts wherever and whenever is convenient for you, at your own pace. No access to the internet? No problem! Lesson transcripts are printable so you can create handy reference tools. Once you have reviewed this chapter, you should be able to do the following:

- Define radical functions and equations
- Create graphs of radical functions
- Understand how to rationalize denominators in radical expressions
- Multiply and divide radical expressions
- Follow steps to solve radical equations
- Explain how to solve radical equations with two radical terms
- Describe transformations of radical functions

### 1. What is a Radical Function? - Definition, Equations & Graphs

Radical functions operate very differently than regular functions. This lesson covers the definitions, equations, and graphs that you will need to know to be successful with radical functions.

### 2. Rationalizing Denominators in Radical Expressions

Radical expressions containing denominators are not simplified completely unless the denominator is free of radical symbols. This lesson will teach you how to remove a radical from the denominator of a fraction through a process called rationalizing the denominator.

### 3. Multiplying then Simplifying Radical Expressions

Multiplying 2 or more radical expressions uses the same principles as multiplying polynomials, with a few extra rules for dealing with the radicals. This lesson will teach you how to multiply and then simplify radical expressions.

### 4. Dividing Radical Expressions

When dividing radical expressions, we use the quotient rule. This lesson will describe the quotient rule and how to use it to solve these radical expressions.

### 5. Solving Radical Equations: Steps and Examples

Solving radical equations is not any more difficult than solving other algebraic equations. This lesson will show you how to solve equations containing a square root and give some real-world examples.

### 6. Solving Radical Equations with Two Radical Terms

Solving equations with two radical terms takes some patience and care, but it really is not difficult. This lesson will show you the steps to solve these more complicated equations plus give you some examples to follow.

### 7. Transformations of Radical Functions

A radical function is a function with a square root or other radical in it. Learn how changes to the equations of radical functions map onto changes in the graphs of the functions in this lesson.

### 8. Practice Problem Set for Radical Expressions & Functions

If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.

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### Other Chapters

Other chapters within the Math 101: College Algebra course

- Foundations of Linear Equations
- Matrices and Absolute Value
- Inequalities
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Functions
- Rational Expressions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101