# Ch 20: 6th-8th Grade Math: Roots & Radical Expressions

### About This Chapter

## 6th-8th Grade Math: Roots & Radical Expressions - Chapter Summary

This chapter uses a series of video lessons taught by expert instructors to educate students on how to work with roots and radical expressions. These video lessons consist of lectures and example problems students can work on with the instructors. Along with the lessons, students can take short quizzes to help them retain the material presented. Some of the topics that will be covered include: finding square and cube roots, identifying radicands, and other mathematical operations used when simplifying radical expressions.

## Chapter Lessons and Objectives

Lesson | Objective |
---|---|

How to Find the Square Root of a Number | Instructors in this video lesson teach students how to find the square roots of numbers. |

Estimating Square Roots | This video lesson shows students how to estimate the square roots of numbers. |

Simplifying Square Roots When not a Perfect Square | Instructors demonstrate how to find the square root of a number when the number is not a perfect square. |

Simplifying Expressions Containing Square Roots | This lesson explains how to use square roots when simplifying expressions. |

Radicands and Radical Expressions | Instructors define radicands, show how to find the radicand of a radical expression and how to determine if the solution is a real number. |

Evaluating Square Roots of Perfect Squares | This video lesson shows how to simplify radical expressions with a perfect-square radicand. |

Factoring Radical Expressions | Instructors in this video review the product rule of radicals and how to multiply with radical notations. |

Simplifying Square Roots of Powers in Radical Expressions | This video lesson teaches students how to simplify radical expressions when the radicands are powers. |

Multiplying then Simplifying Radical Expressions | Instructors demonstrate how to multiply radical expressions when simplifying. |

Dividing Radical Expressions | This video lesson shows how to divide radical expressions when simplifying. |

Simplify Square Roots of Quotients | Instructors teach students how to simplify square roots of quotients. |

Rationalizing Denominators in Radical Expressions | Instructors in this video lesson show how to rationalize denominators in radical expressions. |

Addition and Subtraction Using Radical Notation | This video lesson teaches students how to use distributive laws to simplify radical expressions, adding and subtracting radical notations. |

Multiplying Radical Expressions with Two or More Terms | This lesson explains how to multiply expressions with radicals, some with multiple terms. |

Solving Radical Equations: Steps and Examples | Instructors teach the principle of squaring once, and how to use it when solving radical equations with one or two isolated radical terms. |

Solving Radical Equations with Two Radical Terms | This video lesson demonstrates the principle of squaring twice when solving radical equations with two radical terms. |

How to Find the Cube Root of a Number | Instructors in this video lesson show students how to find the cube roots of numbers. |

### 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.

### 17. How to Find the Cube Root of a Number

After watching this video lesson, you will understand the process of finding the cube root of a number. Learn which numbers have an easy cube root to find and what the cube root means.

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### Other Chapters

Other chapters within the 6th-8th Grade Math: Practice & Review course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Divisibility
- 6th-8th Grade Math: Properties of Numbers
- 6th-8th Grade Math: Number Theory
- 6th-8th Grade Math: Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 6th-8th Grade Math: Simplifying Whole Number Expressions
- 6th-8th Grade Math: Negative Numbers
- 6th-8th Grade Math: Absolute Value
- 6th-8th Grade Math: Integers
- 6th-8th Grade Math: Rational Numbers
- 6th-8th Grade Math: Inequalities
- 6th-8th Grade Math: Introduction to Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Percents
- 6th-8th Grade Math: Exponents & Exponential Expressions
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- 6th-8th Grade Algebra: Basic Algebraic Expressions
- 6th-8th Grade Algebra: Algebraic Distribution
- 6th-8th Grade Algebra: Writing & Solving One-Step Equations
- 6th-8th Grade Algebra: Writing & Solving Two-Step Equations
- 6th-8th Grade Algebra: Simplifying & Solving Rational Expressions
- 6th-8th Grade Math: The Coordinate Graph
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- 6th-8th Grade Math: Solving Math Word Problems
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Introduction to Geometric Figures
- 6th-8th Grade Geometry: Angles
- 6th-8th Grade Measurement: Units of Measurement
- 6th-8th Grade Geometry: Triangles
- 6th-8th Grade Geometry: Quadrilaterals
- 6th-8th Grade Geometry: Circles
- 6th-8th Grade Geometry: Circular Arcs & Measurement
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- 6th-8th Grade Geometry: Symmetry, Similarity & Congruence
- 6th-8th Grade Geometry: Transformations
- 6th-8th Grade Geometry: Triangle Theorems & Proofs
- 6th-8th Grade Geometry: Similar Polygons
- 6th-8th Grade Geometry: The Pythagorean Theorem
- 6th-8th Grade Math: Data & Graphs
- 6th-8th Grade Math: Probability
- 6th-8th Grade Math: Statistics
- 6th-8th Grade Math: Rates, Ratios & Proportions
- 6th-8th Grade Math: Money
- 6th-8th Grade Math: Consumer Math
- 6th-8th Grade Math: Number Sequences
- 6th-8th Grade Math: Sets
- 6th-8th Grade Algebra: Monomials & Polynomials