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Ch 20: 8th Grade Math: Roots & Radical Expressions

About This Chapter

Help your 8th graders get up to speed on roots and radical expressions with these convenient and entertaining video lessons. Check your students' mastery of these concepts with the self-assessment quizzes that accompany each lesson.

8th Grade Math: Roots and Radical Expressions - Chapter Summary

The fun video lessons and quick quizzes in this chapter are useful for helping your 8th grader review and practice operations involving roots and radical expressions. Students can watch these engaging videos to learn how to estimate square roots, factor radical expressions and find cube roots. The self-assessment quizzes that come with each lesson and the chapter exam are handy tools for checking your student's progress or understanding of critical concepts.

Chapter Lessons and Objectives

Lesson Objective
How to Find the Square Root of a Number Lesson uses examples to show students how to find a number's square root.
Estimating Square Roots Students learn the process required to estimate square roots.
Simplifying Square Roots When not a Perfect Square Instructors show students what to do when a square root isn't a perfect square.
Simplifying Expressions Containing Square Roots Videos provide instructions on simplifying expressions that have square roots.
Radicands and Radical Expressions Students learn to find radicands of radical expressions and determine if an expression is representing a real number.
Evaluating Square Roots of Perfect Squares This lesson shows the method for simplifying radical expressions with perfect square radicands.
Factoring Radical Expressions Students learn the product rule for radicals and how to use it in multiplication operations with radical notation.
Simplifying Square Roots of Powers in Radical Expressions Using examples, instructors show how to simplify radical expressions that have radicands as powers.
Multiplying then Simplifying Radical Expressions Students practice multiplying radical expressions and then simplifying them.
Dividing Radical Expressions The video provides step-by-step directions for dividing radical expressions.
Simplify Square Roots of Quotients Lessons use examples to describe how to simplify the square roots of quotients.
Rationalizing Denominators in Radical Expressions Students learn how to rationalize denominators of radical expressions.
Addition and Subtraction Using Radical Notation Instructors teach the steps required to add and subtract with radical notation and describe how the distributive laws are used to simplify.
Multiplying Radical Expressions with Two or More Terms Students look at radical expressions that have more than one term and learn how to multiply them.
Solving Radical Equations: Steps and Examples Video shows how to use the principle of squaring once when solving radical equations with a couple isolated radical terms.
Solving Radical Equations with Two Radical Terms Students demonstrate the method for solving radical equations that have two radical terms by using the principle of squaring twice.
How to Find the Cube Root of a Number Instructors use examples to describe the process of finding the cube root of a number.

16 Lessons in Chapter 20: 8th Grade Math: Roots & Radical Expressions
Test your knowledge with a 30-question chapter practice test
How to Find the Square Root of a Number

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.

Estimating Square Roots

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.

Simplifying Square Roots When not a Perfect Square

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.

Simplifying Expressions Containing Square Roots

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.

Radicands and Radical Expressions

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.

Evaluating Square Roots of Perfect Squares

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.

Factoring Radical Expressions

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.

Simplifying Square Roots of Powers in Radical Expressions

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.

Multiplying then Simplifying Radical Expressions

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.

Dividing 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.

Simplify Square Roots of Quotients

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.

Rationalizing Denominators in Radical Expressions

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.

Addition and Subtraction Using Radical Notation

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.

Multiplying Radical Expressions with Two or More Terms

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.

Solving Radical Equations: Steps and Examples

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.

Solving Radical Equations with Two Radical Terms

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the 8th Grade Math: Practice & Review course

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