# Ch 7: Rational Roots

### About This Chapter

## Rational Roots - Chapter Summary

The short video lessons in this chapter will refresh, and perhaps improve, your skills in working with rational roots. Instructors guide you through a variety of problems, such as simplifying imperfect square roots and solving radical equations with two radical terms. You'll also study radicands, radical expressions and radical notation. In addition to being able to find a number's square root, you'll be able to do the following after watching the videos:

- Estimate square roots
- Simplify square roots and expressions with square roots
- Factor radical expressions
- Evaluate square roots of perfect squares
- Simplify square roots of powers in radical expressions
- Multiply and divide radical expressions
- Simplify the square roots of quotients
- Rationalize denominators in radical expressions
- Use radical notation to add and subtract
- Solve radical equations

As you study rational roots, be sure to take advantage of the tools we offer with our lessons. The videos, developed by professional instructors, offer a jump feature in the timeline that you can use to rewatch explanations of concepts or example problems. We provide transcripts of our lessons as well and these highlight key terms for easy reference. Take the self-assessment quizzes included with all lessons to gauge your understanding of rational roots.

### 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.

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### Other Chapters

Other chapters within the Accuplacer Math: Quantitative Reasoning, Algebra, and Statistics Placement Test Study Guide course

- Computation with Integers
- Negative Numbers
- Absolute Value
- Solving & Graphing Rational Numbers
- Proportions, Ratios & Averages
- Simplifying Algebraic Fractions
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Overview of Inequalities
- Systems of Equations & Inequalities
- Algebraic Word Problems
- Fundamental Algebraic Expressions
- Algebraic Distribution
- Writing Algebraic Expressions
- Writing & Solving One-Step Equations
- Writing & Solving Multi-Step Equations
- Probability, Chance & Fundamental Counting Techniques
- Interpreting Visual Displays of Data
- Basic Geometry Calculations
- Pythagorean Theorem
- Coordinate & Transformational Geometry
- Accuplacer Math: Quantitative Reasoning, Algebra, and Statistics Placement Test Flashcards