# Ch 13: TExES Math 4-8: Radical Expressions

### About This Chapter

## TExES Math 4-8: Radical Expressions - Chapter Summary

The lessons in this test prep chapter refresh your ability to solve radical expressions. The videos and text transcripts cover finding the square root of a number, simplifying square roots when they're not a perfect square and simplifying complex expressions that contain square roots. Additional topics explained here include radicands and radical expressions and evaluating the square roots of perfect squares. After completing the chapter, you should be able to:

- Factor radical expressions
- Simplify square roots of powers in radical expressions
- Multiply and then simplify radical expressions
- Divide radical expressions
- Simplify square roots of quotients
- Rationalize denominators in radical expressions
- Use radical notation to do addition and subtraction
- Multiply radical expressions with two or more terms

Our qualified instructors guide you through each topic in preparation for the test. Jump to specific video sections with the timeline and use the text transcripts to review the concepts you need to focus on in order to strengthen your mastery. Before taking the exam, answer the questions on the lesson quizzes and chapter test to ensure you're ready.

### 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. 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.

### 3. Simplifying Complex Expressions That Contain Square Roots

Watch this video lesson to learn the process of simplifying square roots in complex expressions. Learn how to use the letter i and how to reduce your square roots.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

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### Other Chapters

Other chapters within the TExES Mathematics 4-8 Exam (115): Study Guide & Review course

- About the TExES Math 4-8 Exam
- TExES Math 4-8: Basic Arithmetic
- TExES Math 4-8: Number Theories & Computation Strategies
- TExES Math 4-8: Math Expressions & Formulas
- TExES Math 4-8: Decimals
- TExES Math 4-8: Fractions
- TExES Math 4-8: Percent Notation
- TExES Math 4-8: Calculations, Ratios & Proportions
- TExES Math 4-8: Real Numbers
- TExES Math 4-8: Sequences & Series
- TExES Math 4-8: Exponents & Exponential Expressions
- TExES Math 4-8: Exponentials & Logarithms
- TExES Math 4-8: Algebraic Expressions & Equations
- TExES Math 4-8: Functions
- TExES Math 4-8: Trigonometric Functions & Graphs
- TExES Math 4-8: Graphing Piecewise Functions
- TExES Math 4-8: Absolute Value Equations
- TExES Math 4-8: Solving & Graphing Inequalities
- TExES Math 4-8: Imaginary & Complex Numbers
- TExES Math 4-8: Linear Equations
- TExES Math 4-8: Quadratic Equations
- TExES Math 4-8: Measurement & the Metric System
- TExES Math 4-8: Properties of Geometric Shapes
- TExES Math 4-8: Triangles, Theorems & Proofs
- TExES Math 4-8: Three-Dimensional Geometric Figures
- TExES Math 4-6: The Coordinate System
- TExES Math 4-8: Basic Geometric Constructions
- TExES Math 4-8: Summarizing Data
- TExES Math 4-8: Organizing & Displaying Data
- TExES Math 4-8: Mathematical Probability
- TExES Math 4-8: Mathematical Processes & Perspectives
- TExES Math 4-8: Mathematical Learning & Instruction
- TExES Math 4-8: Mathematical Assessments
- TExES Mathematics 4-8 Flashcards