# Ch 27: THEA Test: Radical Expressions

### About This Chapter

## THEA Test: Radical Expressions - Chapter Summary

This chapter provides the comprehensive overview of radical expressions you need to answer related questions on the THEA test in Texas. After reviewing the lessons, you will be able to:

- Simplify square roots
- Understand division and reciprocals of radical expressions
- Evaluate square roots of perfect squares and factor radical expressions
- Divide or multiply then simplify radical expressions
- Rationalize denominators in radical expressions and simplify square roots of quotients
- Add and subtract using radical notation and multiply radical expressions using two or more terms
- Solve radical equations containing a square root or two radical terms

The lessons give you an opportunity to learn from expert instructors from the comfort of your home or on the go via your smartphone or tablet. If you have any questions about lesson concepts, submit them any time.

### THEA Test: Radical Expressions Objectives

The THEA test is designed to ensure prospective college freshman have the reading, math and writing comprehension skills needed to perform well at a Texas public college or university. It consists of three sections that are scored separately. This chapter's topics are found in the mathematics section, which consists of 50 multiple-choice questions and requires a minimum score of 230 to pass.

In addition to watching the videos in this chapter, you can take short quizzes and a chapter exam to reinforce lesson concepts. If you want to review specific information within the lessons, take advantage of timelines located below the videos that allow you to easily identify and skip to key topics.

### 1. 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.

### 2. Division and Reciprocals of Radical Expressions

Watch this video lesson to learn what you need to do when dividing radical expressions. Learn what you need to look out for before you divide and why you can't leave your radical in your denominator.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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 THEA Test: Practice & Study Guide course

- THEA Test: Understanding Words & Phrases
- THEA Test: Analyzing Literature
- THEA Test: Reading Comprehension & Interpretation
- THEA Test: Point of View & Meaning in Literature
- THEA Test: Drawing Conclusions from Ideas in Text
- THEA Test: Using Critical Thinking to Evaluate Writing
- THEA Test: Understanding Reading Assignments
- THEA Test: Writing Style
- THEA Test: Writing Organization
- THEA Test: Writing Grammar & Mechanics
- THEA Test: Using Verbs
- THEA Test: Using Modifiers
- THEA Test: Using Nouns & Pronouns
- THEA Test: Proofreading & Editing Your Writing
- THEA Test: Fundamental Arithmetic
- THEA Test: Simplifying Whole Number Expressions
- THEA Test: Negative Numbers
- THEA Test: Absolute Value
- THEA Test: Properties of Basic Math
- THEA Test: Solving Word Problems
- THEA Test: Fractions
- THEA Test: Decimals & Percentages
- THEA Test: Ratios & Proportions
- THEA Test: Units of Measurement
- THEA Test: Scientific Notation
- THEA Test: Radicals & Square Roots
- THEA Test: Exponents
- THEA Test: Calculating & Plotting Data
- THEA Test: Solving Rational Equations
- THEA Test: Graphing Linear Equations
- THEA Test: Principles of Algebra
- THEA Test: Algebraic Expressions & Equations
- THEA Test: Word Problems in Algebra
- THEA Test: Properties of Functions
- THEA Test: Quadratic Equations
- THEA Test: Two-Variable Equations & Systems of Equations
- THEA Test: Properties of Polynomial Functions
- THEA Test: Properties & Theorems of Geometry
- THEA Test: Principles of Geometry
- THEA Test: Area, Perimeter & Volume in Geometry
- THEA Test: Problem Solving in Math
- THEA Test Flashcards