# Ch 14: SBA Math - Grade 8: Roots & Radical Expressions

### About This Chapter

## SBA Math Grade 8: Roots and Radical Expressions - Chapter Summary

The lessons in this chapter can help your son or daughter review what they learned about roots and radical expressions as they prepare to take the SBA Math Grade 8 Exam. They'll find everything they need to know in the videos, including:

- Finding and estimating square roots
- Simplifying square roots and expressions containing square roots
- Radicands and radical expressions
- Performing mathematical operations with radical expressions
- Evaluating square roots of perfect squares
- Factoring radical expressions
- Solving radical equations
- Cube root

Our expert instructors guide your child through all the concepts they need to know and show them how to use them, in preparation for the test. Quizzes can be taken after each lesson. Your child can even ask questions by using the 'ask-an-expert' dashboard feature.

### SBA Math Grade 8: Roots and Radical Expressions Chapter

The SBA Math Grade 8 Exam is an evaluation of every mathematical topic taught in the eighth-grade mathematics curriculum. The results will indicate whether your child is performing at grade level. The lessons in this Roots and Radical Expressions chapter fall within the Concepts and Procedures objective, which makes up the majority of the test questions. The self-assessment quizzes that come with the videos give your child a good chance to see what they know and what they still need to study. They can also practice answering the kinds of questions that will be on the exam.

The test lasts for three and a half hours and includes several kinds of questions. Some will be multiple-choice, showing them a question or problem and several possible responses from which they must choose the correct one. They will also be given 'tasks' which are mathematics problems to solve, and a more complex 'performance event' which involves solving a real-world type of mathematics problem.

### 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. Cube Root: Definition, Formula & Examples

In this lesson, we're going to discover the world of cube roots! By the time we're done, you should be able to define what a cube root is, explain how to solve for the cube root of a number, and be familiar with several common cube roots.

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### Other Chapters

Other chapters within the Smarter Balanced Assessments - Math Grade 8: Test Prep & Practice course

- SBA Math - Grade 8: Basic Arithmetic Operations
- SBA Math - Grade 8: Logic & Mathematical Reasoning
- SBA Math - Grade 8: Number Theory
- SBA Math - Grade 8: Introduction to Fractions
- SBA Math - Grade 8: Operations with Fractions
- SBA Math - Grade 8: Ratios, Rates & Proportions
- SBA Math - Grade 8: Percents
- SBA Math - Grade 8: Introduction to Decimals
- SBA Math - Grade 8: Operations with Decimals
- SBA Math - Grade 8: The Coordinate Graph
- SBA Math - Grade 8: Inequalities
- SBA Math - Grade 8: Factoring
- SBA Math - Grade 8: Rational Numbers
- SBA Math - Grade 8: Exponents & Exponential Expressions
- SBA Math - Grade 8: Basic Algebraic Expressions
- SBA Math - Grade 8: Writing Algebraic Expressions
- SBA Math - Grade 8: Algebraic Distribution
- SBA Math - Grade 8: Rational Expressions
- SBA Math - Grade 8: Linear Equations
- SBA Math - Grade 8: Systems of Linear Equations
- SBA Math - Grade 8: Properties of Functions
- SBA Math - Grade 8: Graphing Functions
- SBA Math - Grade 8: Symmetry, Similarity & Congruence
- SBA Math - Grade 8: Lines & Angles
- SBA Math - Grade 8: Perimeter & Area
- SBA Math - Grade 8: Surface Area & Volume of Geometric Solids
- SBA Math - Grade 8: Triangles
- SBA Math - Grade 8: Triangle Theorems & Proofs
- SBA Math - Grade 8: Similar Polygons
- SBA Math - Grade 8: The Pythagorean Theorem
- SBA Math - Grade 8: Transformations
- SBA Math - Grade 8: Data & Graphs
- SBA Math - Grade 8: Statistics
- SBA Math - Grade 8: Probability
- SBA Math - Grade 8: Rate of Change
- Smarter Balanced Assessments - Math Grade 8 Flashcards