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Ch 15: MTTC Math (Secondary): Roots & Radical Expressions

About This Chapter

Build upon what you've previously studied about roots and radical expressions by reviewing this chapter's video lessons on the subject. The lessons and quizzes might prepare you for some of the questions on the MTTC Math (Secondary) examination.

MTTC Math (Secondary): Roots and Radical Expressions - Chapter Summary

When you watch the online video lessons in this chapter, you can re-discover simple techniques for estimating, evaluating and simplifying square roots. The lessons explore square root operations, inverse operations, the quotient rule and the product rule for radicals. In addition to studying several examples of these concepts and operations, and you'll have opportunities to complete practice problems as you get set for the MTTC Math (Secondary) examination. This chapter's lessons might help you to:

  • Find and estimate the square root of a number
  • Simplify and evaluate the square roots of perfect and imperfect squares
  • Write expressions that include square roots
  • Define radicands and radicals
  • Factor to simplify a radical expression
  • Simplify the square roots of powers
  • Multiply, divide and simplify radical expressions, and multiply expressions with two or more terms
  • Use the quotient rule to simplify square roots
  • Rationalize the denominator
  • Add and subtract radical expressions
  • Solve radical equations with two or more terms
  • Define a cube root

The interactive video lessons are taught by instructors who are education leaders as well as mathematics experts. As the instructors review the above math terms and concepts, you can reinforce your own knowledge prior to taking the MTTC Math (Secondary) examination. Use the video tags to promptly find information, or you might consult the written transcripts instead. Study whenever it's convenient, ask questions about roots and radical expressions, and test your comprehension with the lesson quizzes.

MTTC Math (Secondary): Roots and Radical Expressions Chapter Objectives

The material in this chapter is reflected in the 'Patterns, Algebraic Relationships and Functions' section of the four-part MTTC Math (Secondary) examination. The section makes up to 28% of the overall examination score. Use what you've learned here to demonstrate your mastery of roots, radical expressions and other concepts and to qualify for a mathematics teaching endorsement in Michigan.

You may take either the paper-based or computer-based versions of the MTTC Math (Secondary) examination. The computer-administered version takes up to two hours and 30 minutes to finish, whereas the paper-based version could last up to four hours and 30 minutes. Each version contains 80 multiple-choice questions.

17 Lessons in Chapter 15: MTTC Math (Secondary): 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.

Cube Root: Definition, Formula & Examples

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.

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 MTTC Mathematics (Secondary) (022): Practice & Study Guide course

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