# Ch 12: ACT Math - Radicals: Help and Review

### About This Chapter

## Who's it for?

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

- Students who have fallen behind in understanding square roots or dealing with radicals in math
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of preparing for the ACT (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about radicals in math
- Students who struggle to understand their teachers
- Students who attend schools without extra ACT preparation 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 ACT Math - Radicals 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 ACT Math - Radicals chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any radicals 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 radicals unit of a standard ACT prep course. Topics covered include:

- Finding the square root of a number
- Simplifying square roots when not perfect squares
- Working with radicands and radical expressions
- Factoring radical expressions
- Rationalizing denominators within 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.

### 17. Negative Square Root: Definition & Overview

After completing this lesson, you will know how to write the square root of a negative number. You will also be able to complete mathematical operations that involve square roots of negative numbers.

### 18. Radical Expression: Definition & Examples

A radical expression is any mathematical expression containing a radical symbol (√). This lesson will go into more detail about the types of radical expressions and give some examples of how to work with them in mathematics. There will be a quiz at the end of the lesson.

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### Other Chapters

Other chapters within the ACT Prep: Help and Review course

- ACT - About the Test: Help and Review
- ACT English - Section Overview: Help and Review
- ACT English - Punctuation: Help and Review
- ACT English - Grammar and Usage: Help and Review
- ACT English - Sentence Structure: Help and Review
- ACT English - Rhetorical Strategy: Help and Review
- ACT English - Organization: Help and Review
- ACT English - Style: Help and Review
- ACT Math - Overview: Help and Review
- ACT Math - Pre-Algebra: Help and Review
- ACT Math - Algebraic Expressions: Help and Review
- ACT Math - Linear Equations: Help and Review
- ACT Math - Functions: Help and Review
- ACT Math - Absolute Value: Help and Review
- ACT Math - Matrices: Help and Review
- ACT Math - Inequalities: Help and Review
- ACT Math - Probability: Help and Review
- ACT Math - Data and Statistics: Help and Review
- ACT Math - Exponents: Help and Review
- ACT Math - Polynomials and Quadratics: Help and Review
- ACT Math - Rational Equations: Help and Review
- ACT Math - Sequences: Help and Review
- ACT Math - Complex Numbers: Help and Review
- ACT Math - Exponentials and Logarithms: Help and Review
- ACT Math - Coordinate Geometry: Help and Review
- ACT Math - Conic Sections: Help and Review
- ACT Math - Triangles: Help and Review
- ACT Math - Plane Geometry: Help and Review
- ACT Math - Logic in Mathematics: Help and Review
- ACT Math - Trigonometry: Help and Review
- ACT Science Reasoning - Overview: Help and Review
- ACT Science Reasoning - Fundamentals: Help and Review
- ACT Reading - Overview: Help and Review
- ACT Reading - Question Types: Help and Review
- ACT Reading - Understanding Passages: Help and Review
- ACT Reading - Literary Terms: Help and Review
- ACT Reading - Practice: Help and Review
- ACT Writing - Overview: Help and Review
- ACT Writing - Essay Skills: Help and Review
- ACT Writing - Essay Parts: Help and Review
- ACT Writing - Planning: Help and Review
- ACT Writing - Advanced Skills: Help and Review
- ACT Prep Help and Review Flashcards