# Ch 22: Radical Expressions & Equations

### About This Chapter

## Radical Expressions & Equations - Chapter Summary

In this chapter on radical expressions and equations, brief lessons cover topics such as how to multiply radical expressions and how to use distributive laws. Additionally, you can learn about solving radical equations containing two radical terms. Upon completion of the chapter, you should be able to do the following:

- Identify radicands of radical expressions
- Recall the product rule for radicals
- Explain how to simplify radical expressions
- Demonstrate how to divide radical expressions
- Rationalize the denominator of a radical expression
- Explain how to subtract with radical notation
- Discuss multiplying expressions with radicals
- Provide steps for solving radical equations

Our instructors provide helpful examples to assist you with grasping the concepts presented. A brief quiz is available for each lesson to test you on radical expressions and equations. You can make the most of this resource by printing the quiz in worksheet form to study offline.

### 1. Radicands and Radical Expressions

It's easy to see that funky radical symbol and panic just a little bit. There are so many rules that go along with it, it's hard to keep up with them all. This lesson will help by describing what you should do when you are faced with a square root.

### 2. Factoring Radical Expressions

Watch this video lesson to learn how to apply the product rule to your radical expressions. Learn how this product rule actually helps you to simplify your radicals as well.

### 3. Simplifying Square Roots of Powers in Radical Expressions

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. Addition and Subtraction Using Radical Notation

There are specific rules governing adding and subtracting radical expressions. This lesson will describe these rules and give examples of how they are used.

### 8. Multiplying Radical Expressions with Two or More Terms

Multiplying radical expressions with more than two terms can be confusing. This lesson will take some of the confusion away by giving clear steps for multiplying these expressions. It will also provide some examples to help solidify the steps.

### 9. 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.

### 10. 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the MTLE Middle Level Mathematics: Practice & Study Guide course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Properties of Numbers
- Number Theory & Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 5th Grade Math: Simplifying Whole Number Expressions
- Negative Numbers
- 6th-8th Grade Math: Absolute Value
- 6th-8th Grade Math: Integers
- 6th-8th Grade Math: Rational Numbers
- 6th-8th Grade Math: Inequalities
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Introduction to Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Percents
- Working with Rates, Ratios & Proportions
- Practical Applications of Rates, Ratios & Proportions
- Introduction to Exponents
- Working with Exponential Expressions
- Understanding Square Roots & Radical Expressions
- Imaginary & Complex Numbers
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- Basic Algebraic Expressions & Factoring
- Algebraic Distribution
- 6th-8th Grade Algebra: Writing & Solving One-Step Equations
- 6th-8th Grade Algebra: Writing & Solving Two-Step Equations
- 6th-8th Grade Algebra: Simplifying & Solving Rational Expressions
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Algebra: Monomials & Polynomials
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- Rate of Change Basics
- Notation, Sequences & Series
- 6th-8th Grade Measurement: Units of Measurement
- Fundamentals of Geometric Figures & Angles
- Two-Dimensional Shapes
- Circle Geometry
- The Pythagorean Theorem & Trigonometry
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- Congruence & Similarity in Geometry
- 6th-8th Grade Math: The Coordinate Graph
- 6th-8th Grade Geometry: Transformations
- Modeling to Solve Problems
- Basic Probability
- Statistics & Sampling Basics
- MTLE Middle Level Mathematics Flashcards