# Ch 14: Square Roots & Radical Expressions

### About This Chapter

## Square Roots & Radical Expressions - Chapter Summary and Learning Objectives

When describing a person, 'square' and 'radical' are at the opposite ends of the spectrum. In math, however, they are interrelated topics. Make learning about these math concepts enjoyable and rewarding. Lessons reveal information and practice dealing with discovery, estimation and simplification of square roots. Find out how to perform operations on radical expressions through video and transcript instruction that includes plenty of examples. By the time you finish this chapter, you should feel comfortable with the following topics:

Video | Objective |
---|---|

How to Find the Square Root of a Number | Discover ways to find the square roots of numbers. |

Estimating Square Roots | Learn about why and how we estimate square roots. |

Simplifying Square Roots When not a Perfect Square | Practice the steps for simplification of square roots when an imperfect square is involved. |

Simplifying Expressions Containing Square Roots | Explore the methods for simplification of expressions involving square roots. |

Radicands and Radical Expressions | Find out what radicands and radical expressions are and when they might be encountered. |

Evaluating Square Roots of Perfect Squares | Delve into the ways we can evaluate square roots of squares that are perfect. |

Factoring Radical Expressions | Use your factoring skills to work with radical expressions. |

Simplifying Square Roots of Powers in Radical Expressions | Learn the details for simplifying square roots of powers in radical expressions. |

Multiplying then Simplifying Radical Expressions | Practice multiplying first and then simplifying radical expressions. |

Dividing Radical Expressions | Exercise your skills for division of radical expressions. |

Simplify Square Roots of Quotients | Dig into the rules for simplifying square roots of quotients. |

Rationalizing Denominators in Radical Expressions | Explore the methods for rationalizing denominators in radical expressions. |

Addition and Subtraction Using Radical Notation | Use radical notation to add and subtract. |

Multiplying Radical Expressions with Two or More Terms | If there are two or more terms, use the presented steps in this lesson for multiplying radical expressions. |

Solving Radical Equations: Steps and Examples | Study the steps and clear examples to learn about solving radical equations. |

Solving Radical Equations with Two Radical Terms | If there are two radical terms, find out how to solve radical equations with this lesson. |

### 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 Algebra 2 and Trig Textbook course

- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graphing & Working with Trigonometric Functions
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs