# Ch 21: CEOE Middle Level/Intermediate Math: Radical Expressions

### About This Chapter

## CEOE Middle Level/Intermediate Math: Radical Expressions - Chapter Summary

Study.com subject matter experts have put together this series of video lessons to get you ready for CEOE testing. This prep will help you answer questions on things to do with:

- Finding the square root of a number
- Simplification of a square root that is not a perfect square
- Simplification of an expression containing a square root
- Familiarization with radicands and radical expressions
- How to factor radicals
- How to simplify square roots of powers within radicals
- How to multiply and then simplify radical expressions
- Division of radical expressions
- Simplification of quotient square roots
- Rationalizing of denominators in radicals
- Use of radical notation in addition and subtraction
- Multiplication of radical expressions with multiple terms
- The steps for solving radical equations

Lessons consist of short, engaging videos on each of the above topics. The information is broken up into easy-to-digest blocks of material, each with a self-assessment quiz at the end to verify you got it.

### 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 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.

### 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. 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. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 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 OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

- CEOE Middle Level/Intermediate Math: Problem Solving Strategies
- CEOE Middle Level/Intermediate Math: Reasoning & Logic
- CEOE Middle Level/Intermediate Math: Mathematical Modeling
- CEOE Middle Level/Intermediate Math: Real Numbers
- CEOE Middle Level/Intermediate Math: Fractions
- CEOE Middle Level/Intermediate Math: Decimals
- CEOE Middle Level/Intermediate Math: Percentages
- CEOE Middle Level/Intermediate Math: Ratios, Rates & Proportions
- CEOE Middle Level/Intermediate Math: Exponents & Exponential Expressions
- CEOE Middle Level/Intermediate Math: Properties of Real Numbers
- CEOE Middle Level/Intermediate Math: Sequences & Series
- CEOE Middle Level/Intermediate Math: Introduction to Algebra
- CEOE Middle Level/Intermediate Math: Introduction to Functions
- CEOE Middle Level/Intermediate Math: Linear Equations
- CEOE Middle Level/Intermediate Math: Linear Inequalities
- CEOE Middle Level/Intermediate Math: Systems of Equations
- CEOE Middle Level/Intermediate Math: Matrices in Linear Algebra
- CEOE Middle Level/Intermediate Math: Quadratic Functions
- CEOE Middle Level/Intermediate Math: Polynomial Functions
- CEOE Middle Level/Intermediate Math: Rational Expressions
- CEOE Middle Level/Intermediate Math: Absolute Value Functions
- CEOE Middle Level/Intermediate Math: Exponential & Logarithmic Equations
- CEOE Middle Level/Intermediate Math: Measurement
- CEOE Middle Level/Intermediate Math: Area & Perimeter
- CEOE Middle Level/Intermediate Math: Surface Area & Volume
- CEOE Middle Level/Intermediate Math: Foundations of Geometry
- CEOE Middle Level/Intermediate Math: Lines & Angles
- CEOE Middle Level/Intermediate Math: Properties of Triangles
- CEOE Middle Level/Intermediate Math: Similar & Congruent Triangle Proofs
- CEOE Middle Level/Intermediate Math: Right Triangle Proofs
- CEOE Middle Level/Intermediate Math: Quadrilaterals & Polygons
- CEOE Middle Level/Intermediate Math: Circles & Arc of a Circle
- CEOE Middle Level/Intermediate Math: Conic Sections
- CEOE Middle Level/Intermediate Math: Coordinate Geometry
- CEOE Middle Level/Intermediate Math: Transformations in Geometry
- CEOE Middle Level/Intermediate Math: Trigonometry
- CEOE Middle Level/Intermediate Math: Limits
- CEOE Middle Level/Intermediate Math: Rate of Change & Derivatives
- CEOE Middle Level/Intermediate Math: Area Under the Curve & Integrals
- CEOE Middle Level/Intermediate Math: Probability
- CEOE Middle Level/Intermediate Math: Discrete Probability Distributions
- CEOE Middle Level/Intermediate Math: Continuous Probability Distributions
- CEOE Middle Level/Intermediate Math: Overview of Statistics
- CEOE Middle Level/Intermediate Math: Sampling
- CEOE Middle Level/Intermediate Math: Graphs, Charts & Diagrams
- CEOE Middle Level/Intermediate Math: Summarizing Data
- CEOE Middle Level/Intermediate Math: Discrete Mathematics
- OSAT Middle Level/Intermediate Mathematics (CEOE) (125) Flashcards