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Ch 4: CAHSEE Radical Expressions & Equations: Help & Review

About This Chapter

The Problems with Radical Expressions & Equations chapter of this CAHSEE Math Help and Review course is the simplest way to master radical expressions and equations. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of radical expressions and equations.

Who's it for?

Anyone who needs help learning or mastering CAHSEE math material will benefit from taking this course. There is no faster or easier way to prepare for the CAHSEE math exam. Among those who would benefit are:

  • Students who have fallen behind in understanding how to simplify square roots or solve equations containing 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 and equations
  • 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 Problems with Radical Expressions & Equations 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 Problems with Radical Expressions & Equations chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any radical expressions and equations 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 and equations unit of a standard high school math course. Topics covered include:

  • Estimating square roots
  • Evaluating square roots of perfect squares
  • Simplifying square roots when not a perfect square
  • Simplifying complex expressions containing square roots
  • Simplifying square roots of quotients
  • Rationalizing denominators in radical expressions
  • Adding and subtracting radical expressions
  • Multiplying radical expressions with two or more terms
  • Solving radical equations with one or more radical terms

10 Lessons in Chapter 4: CAHSEE Radical Expressions & Equations: Help & Review
Estimating Square Roots

1. 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.

Evaluating Square Roots of Perfect Squares

2. 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.

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.

Simplify Square Roots of Quotients

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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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