About This Chapter
Working with Radical Expressions - Chapter Summary
Watch entertaining video lessons to feel confident that you understand how to work with radical expressions. This chapter offers a comprehensive overview that ensures you're able to simplify square roots of quotients, solve radical equations and rationalize denominators in radical expressions. Completing this chapter also enables you to:
- Find the square root of a number
- Identify radical expressions and radicands
- Factor, multiply, simplify and divide radical expressions
- Simplify radical expressions with square roots of powers
- Use radical notation to add and subtract
- Multiply radical expressions with two or more terms
- Solve radical equations with two radical terms
The fun lessons in this chapter are accessible as short videos that average 8 minutes each and full transcripts you can read online or print. If you want to revisit important portions of lessons, use clickable timelines to skip to key topics within the videos. Multiple-choice quizzes make it easy to gauge your comprehension of the lessons you study. If you want confirmation that you understand how to work with radical expressions, be sure to take the practice chapter exam.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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 within the Pennsylvania Algebra I Keystone Exam: Test Prep & Practice course
- Real Numbers & Expressions
- Understanding Exponential Expressions
- Understanding Absolute Value Expressions
- Estimation & Math Problem-Solving
- Solving Problems with Polynomials
- Solving, Writing & Graphing Linear Equations
- Solving Problems with Systems of Equations
- Solving & Graphing Linear Inequalities
- Understanding Function Basics
- Using Scatter Plots
- Understanding Basic Statistics
- Interpreting & Graphing Data
- Understanding the Probability of Compound Events
- Pennsylvania Algebra I Keystone Exam Flashcards