# Ch 4: ASSET Intermediate Algebra: Simplifying Radical Expressions

### About This Chapter

## ASSET Intermediate Algebra: Simplifying Radical Expressions - Chapter Summary

Each lesson in this chapter about radical expressions is specifically designed to help you prepare for the ASSET Intermediate Algebra exam, which covers a wide variety of topics. Some topics that are talked about in this chapter include:

- Radical expressions and radicands
- Finding a number's square root
- Working with square roots
- Radical expressions and methods for factoring them
- Square roots of perfect squares
- Subtracting and adding using radical expressions
- Square roots of quotients

Our instructors will guide you through the topics that are going to be in the exam, giving you the right preparation and confidence. Additionally, you can use the self-assessment quizzes to check your knowledge of algebra topics.

### ASSET Intermediate Algebra: Simplifying Radical Expressions - Chapter Objectives

The ASSET Intermediate Algebra exam was created to assess your knowledge and skills of algebra. The materials within this chapter are part of the intermediate algebra and coordinate geometry section, which makes up 64% of the entire test. Our lessons help you identify strategies for simplifying radical expressions, so you will be fully prepared for answering related questions on the exam. The format of the exam is multiple-choice.

### 1. How to Find the Square Root of a Number

What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.

### 2. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

### 3. Simplifying Square Roots When not a Perfect Square

Numbers that are imperfect squares are those that, when evaluated, do not give solutions that are integers. The proper mathematical way to simplify these imperfect squares is discussed in this lesson.

### 4. Simplifying Expressions Containing Square Roots

In order to write radical expressions correctly, they have to be written in their simplest form. This lesson will show you how to simplify expressions containing numbers and variables inside a square root.

### 5. 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.

### 6. Evaluating Square Roots of Perfect Squares

Squares and square roots are inverse, or opposite, operations involving radicals. Learn how to determine the square root of perfect squares in this lesson.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Simplify Square Roots of Quotients

The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

### 12. 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.

### 13. 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.

### 14. 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.

### 15. 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.

### 16. 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.

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### Other Chapters

Other chapters within the ASSET Intermediate Algebra Test: Practice & Study Guide course

- ASSET Intermediate Algebra: Graphing Basics
- ASSET Intermediate Algebra: Factoring Polynomials
- ASSET Intermediate Algebra: Linear Equations
- ASSET Intermediate Algebra: Simplifying Rational Expressions
- ASSET Intermediate Algebra: Slope & Distance Formulas
- ASSET Intermediate Algebra: Linear Inequalities
- ASSET Intermediate Algebra Test Flashcards