Ch 6: NMTA Middle Grades Math: Roots & Radical Expressions

About This Chapter

The state of New Mexico has replaced the NMTA Middle Grades Mathematics test with the NES Middle Grades Mathematics exam. Use this chapter to improve your skills solving problems with roots and radical expressions as you prepare for related questions on the NES Middle Grade Mathematics exam.

NES Middle Grades Mathematics: Roots & Radical Expressions - Chapter Summary

This chapter can aid in your review for the National Evaluation Series (NES) Middle Grades Mathematics test by demonstrating the steps used to find square and cubic roots and simplify radical expressions. Watch our expert instructors in this series of lesson videos to prepare for questions about:

  • Finding square and cubic roots
  • Simplifying expressions with roots
  • Factoring radical expressions
  • Rationalizing denominators
  • Multiplying, dividing, adding and subtracting with radical expressions
  • Steps used to solve radical equations

Reinforce your mastery over the material covered in these videos by completing the lesson quizzes. Using the results from your quizzes, find topics you have not mastered and return to the videos to improve you understanding of those topics. If you would benefit from an alternative way of reviewing the material, try reading over the written outlines of the lessons.

NES Middle Grades Mathematics: Roots & Radical Expressions Objectives

The state of New Mexico uses the NES Middle Grades Mathematics to assess educators' mastery over middle grade mathematics before granting them certification. This computer-based exam is composed of 150 multiple-choice questions and is administered in a four-hour and 15 minutes testing session. Of the material covered by this exam you can expect 33% to be in the Algebra and Functions domain. The lesson videos and quizzes of this chapter have been put together to help you improve your abilities solving problems with roots and radical expression so you will be prepared for related questions in this domain.

16 Lessons in Chapter 6: NMTA Middle Grades Math: Roots & Radical Expressions
Test your knowledge with a 30-question chapter practice test
How to Find the Square Root of a Number

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.

Estimating Square Roots

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.

Simplifying Square Roots When not a Perfect Square

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.

Simplifying Expressions Containing Square Roots

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.

Radicands and Radical Expressions

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.

Evaluating Square Roots of Perfect Squares

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.

Factoring Radical Expressions

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.

Simplifying Square Roots of Powers in Radical Expressions

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.

Multiplying then Simplifying Radical Expressions

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.

Dividing 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.

Simplify Square Roots of Quotients

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.

Rationalizing Denominators in Radical Expressions

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.

Addition and Subtraction Using Radical Notation

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.

Multiplying Radical Expressions with Two or More Terms

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.

Solving Radical Equations: Steps and Examples

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.

Solving Radical Equations with Two Radical Terms

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the NMTA Middle Grades Mathematics (203): Practice & Study Guide course

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