# Ch 7: High School Algebra - Radical Expressions: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school algebra I material will benefit from taking this course. There is no faster or easier way to learn high school algebra I. Among those who would benefit are:

- Students who have fallen behind in understanding square roots or other radical expressions
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about radical expressions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the radical expressions chapter exam.

## Why it works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the radical expressions chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any radical expressions question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a radical expressions unit of a standard high school algebra I course. Topics covered include:

- Finding the square root of a number
- Simplifying square roots when not a perfect square
- Identifying radicands and radical expressions
- Factoring radical expressions
- Dividing radical expressions

### 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 High School Algebra I: Help and Review course

- High School Algebra - Basic Arithmetic: Help and Review
- High School Algebra - Solving Math Word Problems: Help and Review
- High School Algebra - Decimals and Fractions: Help and Review
- High School Algebra - Percent Notation: Help and Review
- High School Algebra - Real Numbers: Help and Review
- High School Algebra - Exponential Expressions & Exponents: Help & Review
- Algebraic Equations and Expressions: Help and Review
- High School Algebra - Properties of Functions: Help and Review
- High School Algebra - Matrices and Absolute Value: Help and Review
- High School Algebra - Working With Inequalities: Help and Review
- High School Algebra - Properties of Exponents: Help and Review
- High School Algebra - Complex and Imaginary Numbers: Help and Review
- High School Algebra - Algebraic Distribution: Help and Review
- High School Algebra - Linear Equations: Help and Review
- High School Algebra - Factoring: Help and Review
- Factoring & Graphing Quadratic Equations: Help & Review
- The Properties of Polynomial Functions: Help & Review
- High School Algebra - Rational Expressions: Help and Review
- High School Algebra - Cubic Equations: Help and Review
- High School Algebra - Quadratic Equations: Help and Review
- High School Algebra - Measurement and Geometry: Help and Review
- Ratios, Proportions & Percent in Algebra: Help & Review
- Statistics, Probability and Data in Algebra: Help and Review
- High School Algebra - Well-Known Equations: Help and Review