# Ch 13: CEOE Advanced Math: Roots & Radical Expressions

### About This Chapter

## CEOE Advanced Math: Roots & Radical Expressions - Chapter Summary

Lessons in this chapter explore roots and radical expressions, including simplifying expressions containing square roots, radicands and radical expressions, and evaluating square roots of perfect squares. Also covered are factoring radical expressions, simplifying square roots of powers in radical expressions, and multiplying them simplifying radical expressions. Additionally, by the end of this chapter, you should be familiar with:

- Dividing radical expressions
- Simplify square roots of quotients
- Rationalizing denominators in radical expressions
- Addition and subtraction using radical notation
- Multiplying radical expressions with two or more terms
- Solving radical equations

Short, engaging video lessons make the material fun and interesting. Self-assessment quizzes can be used to test your knowledge, or print them as worksheets to help you study. The jump feature under the Timeline tab allows you to skip directly to main subjects in each video.

### Roots & Radical Expressions - Chapter Objectives

The CEOE Advanced Mathematics exam measures a student's knowledge of subject matter in accordance with Oklahoma educator licensure regulations. The exam measures mathematical processes and number sense; relations functions, and algebra; measurement and geometry; trigonometry and calculus; and probability, statistics, and discrete mathematics. The material covered in this Roots and Radical Expressions chapter is tested in the relations, functions and algebra portion of the CEOE exam, which comprises about 12% of the entire test. The exam includes approximately 80 multiple-choice questions and one open-response question.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 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.

### 14. Cube Root: Definition, Formula & Examples

In this lesson, we're going to discover the world of cube roots! By the time we're done, you should be able to define what a cube root is, explain how to solve for the cube root of a number, and be familiar with several common cube roots.

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### Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

- CEOE Advanced Math: Mathematical Reasoning & Ideas
- CEOE Advanced Math: Origins of Math
- CEOE Advanced Math: Absolute Value
- CEOE Advanced Math: Inequalities
- CEOE Advanced Math: Integers
- CEOE Advanced Math: Operations with Fractions
- CEOE Advanced Math: Operations with Decimals
- CEOE Advanced Math: Percents
- CEOE Advanced Math: Rational & Irrational Numbers
- CEOE Advanced Math: Complex Numbers
- CEOE Advanced Math: Properties of Numbers
- CEOE Advanced Math: Exponents & Exponential Expressions
- CEOE Advanced Math: Number Theory
- CEOE Advanced Math: Vectors, Matrices & Determinants
- CEOE Advanced Math: Properties of Functions
- CEOE Advanced Math: Graphing Functions
- CEOE Advanced Math: The Coordinate Graph & Graph Symmetry
- CEOE Advanced Math: Linear Equations
- CEOE Advanced Math: Systems of Linear Equations
- CEOE Advanced Math: Quadratic Functions
- CEOE Advanced Math: Polynomial Functions Basics
- CEOE Advanced Math: Higher-Degree Polynomial Functions
- CEOE Advanced Math: Piecewise, Absolute Value & Step Functions
- CEOE Advanced Math: Rational Expressions & Function Graphs
- CEOE Advanced Math: Exponential & Logarithmic Functions
- CEOE Advanced Math: Measurement
- CEOE Advanced Math: Perimeter & Area
- CEOE Advanced Math: Symmetry, Similarity & Congruence
- CEOE Advanced Math: Properties of Lines
- CEOE Advanced Math: Angles
- CEOE Advanced Math: Triangles
- CEOE Advanced Math: Triangle Theorems & Proofs
- CEOE Advanced Math: Similar Polygons
- CEOE Advanced Math: The Pythagorean Theorem
- CEOE Advanced Math: Circles
- CEOE Advanced Math: Circular Arcs & Measurement
- CEOE Advanced Math: Transformations
- CEOE Advanced Math: Analytic Geometry & Conic Sections
- CEOE Advanced Math: Trigonometric Functions
- CEOE Advanced Math: Trigonometric Graphs
- CEOE Advanced Math: Trigonometric Applications
- CEOE Advanced Math: Limits
- CEOE Advanced Math: Continuity
- CEOE Advanced Math: Rate of Change
- CEOE Advanced Math: Derivative Calculations & Rules
- CEOE Advanced Math: Graphing & Applying Derivatives
- CEOE Advanced Math: Area Under the Curve & Integrals
- CEOE Advanced Math: Integration Techniques
- CEOE Advanced Math: Differential Equations
- CEOE Advanced Math: Data & Graphs
- CEOE Advanced Math: Samples & Populations
- CEOE Advanced Math: Probability
- CEOE Advanced Math: Sets
- CEOE Advanced Math: Statistics
- CEOE Advanced Math: Number Patterns & Sequences
- CEOE Advanced Math: Number Patterns & Series
- CEOE Advanced Math: Discrete Math
- OSAT Advanced Mathematics (CEOE) (111) Flashcards