# Ch 6: Problems with Radical Expressions & Equations

### About This Chapter

## Problems with Radical Expressions and Equations - Chapter Summary

The video lessons available through this chapter can help you understand how to evaluate problems with radical expressions, such as square roots. Knowledgeable instructors present these lessons with practice problems that can prepare you for the questions on the NY Integrated Algebra Regents exam. You'll explore topics that include:

- Estimating square roots
- Evaluating the square roots of perfect and non-perfect squares
- Simplifying complex expressions that contain square roots
- Solving the square roots of quotients
- Rationalizing denominators in radical expressions
- Adding and subtracting using radical notation
- Multiplying radical expressions with more than two terms
- Solving radical equations with two radical terms

Instructors guide you through each concise, interactive video lesson in the chapter. You can access lesson transcripts if you have further questions about any of the content. You can also take self-assessment quizzes that emulate the problems you could find on the actual Regents exam.

### Problems with Radical Expressions and Equations Objectives

Receiving a Regents Diploma in the state of New York requires you to pass a series of five tests, including the Integrated Algebra Regents exam. You'll need to score a 65 or higher to pass this particular test. You'll have to answer approximately 40 questions split into four parts. The time limit is three hours.

Although most of the Integrated Algebra Regents exam is multiple choice, some questions require you to fill in the answers. You also might need to produce graphs and charts on certain questions. Important concepts featured on the exam include number theory, operations, expressions, equations, coordinate geometry and trigonometric functions.

### 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.

### 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.

### 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. 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.

### 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.

### 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.

### 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.

### 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.

### 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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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards