# Ch 22: MTLE Mathematics: Radical Expressions

### About This Chapter

## MTLE Mathematics: Radical Expressions - Chapter Summary

This chapter is all you need to get ready for the content within the MTLE Mathematics exam that deals with radical expressions, giving adequate attention to each of the following topics:

- Multiplying and dividing radical expressions
- Adding and subtracting radical expressions
- Solving rational equations
- Division and reciprocals of rational expressions
- Simplifying complex rational expressions
- Graphing rational functions that have linear polynomials
- Asymptotes, domain, and range
- Finding slant asymptotes of rational functions
- Expressions of rational functions

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### 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. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

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### Other Chapters

Other chapters within the MTLE Mathematics: Practice & Study Guide course

- MTLE Mathematics: Basic Arithmetic Operations
- MTLE Mathematics: Properties of Real Numbers
- MTLE Mathematics: Operations with Real Numbers
- MTLE Mathematics: Fractions
- MTLE Mathematics: Decimals
- MTLE Mathematics: Percents
- MTLE Mathematics: Ratios, Rates & Proportions
- MTLE Mathematics: Exponents & Exponential Expressions
- MTLE Mathematics: Mathematical Reasoning & Problem Solving
- MTLE Mathematics: Complex Numbers
- MTLE Mathematics: Sequences & Series
- MTLE Mathematics: Functions
- MTLE Mathematics: Algebraic Expressions & Equations
- MTLE Mathematics: Exponential & Logarithmic Functions
- MTLE Mathematics: Vector Operations
- MTLE Mathematics: Matrices in Linear Algebra
- MTLE Mathematics: Linear Functions
- MTLE Mathematics: Linear Inequalities
- MTLE Mathematics: Quadratic Functions
- MTLE Mathematics: Polynomial Functions
- MTLE Mathematics: Rational Expressions
- MTLE Mathematics: Absolute Value Functions
- MTLE Mathematics: Continuity & Limits
- MTLE Mathematics: Rate of Change & Derivatives
- MTLE Mathematics: Area Under the Curve & Integrals
- MTLE Mathematics: Trigonometric Functions
- MTLE Mathematics: Solving Trigonometric Equations
- MTLE Mathematics: Trigonometric Identities
- MTLE Mathematics: Principles of Measurement
- MTLE Mathematics: Area & Perimeter
- MTLE Mathematics: Surface Area & Volume
- MTLE Mathematics: Foundations of Geometry
- MTLE Mathematics: Lines & Angles
- MTLE Mathematics: Properties of Triangles
- MTLE Mathematics: Similar & Congruent Triangle Proofs
- MTLE Mathematics: Right Triangle Proofs
- MTLE Mathematics: Quadrilaterals & Polygons
- MTLE Mathematics: Circles & Arc of a Circle
- MTLE Mathematics: Coordinate Geometry
- MTLE Mathematics: Geometric Transformations
- MTLE Mathematics: Parametric, Polar & Vector Functions
- MTLE Mathematics: Organizing Data
- MTLE Mathematics: Summarizing & Analyzing Data
- MTLE Mathematics: Random Sampling
- MTLE Mathematics: Probability
- MTLE Mathematics: Probability Distributions
- MTLE Mathematics: Discrete Mathematics
- MTLE Mathematics: Mathematical Connections & Communication
- MTLE Mathematics: From Words to Equations, Expressions & Graphs
- MTLE Mathematics: Content Area Reading Skills
- MTLE Mathematics: Instructional Design & Delivery
- MTLE Mathematics: Teaching & Assessing Diverse Learners
- MTLE Mathematics Flashcards