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Ch 7: High School Algebra: Radical Expressions

About This Chapter

Watch radical expressions video lessons and learn square roots, radical notation, radical equations and more. Take the quizzes that follow each lesson to test your knowledge of radical expressions.

High School Algebra I: Radical Expressions - Chapter Summary

The lessons in this chapter provide detailed instruction in the function of radical expressions. The lessons are short, but instructors include lots of examples to help you master the concepts. You'll get to know the basic form of radical expressions. Instructors will also direct you to methods of solving equations with radical expressions. This chapter can help you understand the following:

  • Square roots
  • Radicands
  • Radical notation
  • Radical equations

Video Objective
Finding Square Roots Learn how to find the square root of a number
Radicands and Radical Expressions Review ways to identify radicands of radical expressions and determine whether a radical expression represents a real number
Evaluating Square Roots of Perfect Squares Take a look at methods for simplifying a radical expression with a perfect square radicand
Addition and Subtraction Using Radical Notation Understand the process of adding and subtracting radical notation, using the distributive laws to simplify
Multiplying Radical Expressions with Two or More Terms Find out how to multiply expressions involving radicals, where some of the expressions contain more than one term
Solving Radical Equations Learn to solve radical equations with one or two radical terms isolated, using the principle of squaring once
Solving Radical Equations with Two Radical Terms Explore methods for solving radical equations with two radical terms, using the principle of squaring twice

17 Lessons in Chapter 7: High School Algebra: Radical Expressions
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.

Division and Reciprocals of Radical Expressions

5. Division and Reciprocals of Radical Expressions

Watch this video lesson to learn what you need to do when dividing radical expressions. Learn what you need to look out for before you divide and why you can't leave your radical in your denominator.

Radicands and Radical Expressions

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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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