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DrDelMath

Intermediate Algebra 5th Edition
by Elayn Martin-Gay
SUMMARY

Chapter 7: Rational Exponents, Radicals, and Complex Numbers

Section 7.1: Radicals and Radical Functions

Textbook Objectives
  1. Find square roots.
  2. Approximate roots.
  3. Find cube roots.
  4. Find nth roots.

Exponents: Powers, Products, and Quotients

This symbol radical symbol is called a radical.

An expression of the form radical expression or more generally of the form general radical expression is called a radical expression. The expression b beneath the radical symbol is called the radicand and the small number in the "vee" of the radical symbol is called the index. If no index is written, the index is presumed to be 2.

When the index is 2 and the radicand is non-negative, the symbol radical expression means the principal square root of the radicand b. Therefore radical expression is the positive number whose square is the radicand b. Symbollically this is can be expressed as radical squared.

About Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page 418.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 12
Section 7.1 Exercise Set: 1 - 12, 13 - 18, 19, 21, 23, 25, 27, 29 - 42, 43 - 52.

 

Section 7.2: Rational Exponents

Textbook Objectives
  1. Understand the meaning of XXXXXXXXX.
  2. Understand the meaning of XXXXXXXXX.
  3. Understand the meaning of XXXXXXXXX.
  4. Use rule of exponents to simplify expressions that contain rational exponents.
  5. Use rational exponents to simplify radical expressions.

Exponents: Powers, Products, and Quotients

About Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page 426.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 12.
Section 7.2 Exercise Set: 1 - 16, 17 - 28, 1 - 29, 41 - 59 (all odd numbered), 61, 62, 63, 65,67, 69, 71, 73, - 84, 85 - 98.

 

Section 7.3: Simplifying Radical Expressions

Textbook Objectives
  1. Use the product rule for radicals.
  2. Use the quotient rule for radicals
  3. Simplify radicals.
  4. Use the distance and midpoint formula
Additional Goals
  1. Know the product rule for radicals.
  2. Know the quotient rule for radicals.
  3. Know the midpoint formula.
  4. Know the distance formula.

Exponents: Powers, Products, and Quotients

About Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page 435.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 10.
Section 7.3 Exercise Set: 1, 3, 5, 7, 9, 11, 13, 15, 17, 25, 27, 31, 35, 37, 39, 45, 47, 53, 55, 59, 61, 63, 65, 69, 73, 74, 75, 77, 79, 83, 85, 87, 89, 91, 92

 

Section 7.4: Adding, Subtracting, and Multipying Radical Expressions

Textbook Objectives
  1. Add or subtract radical expressions.
  2. Multiply radical expressions.
Additional Goals
  1. Know the definition of like radicals.

Exponents: Powers, Products, and Quotients

About Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page 440.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check: 1 - 14.
Section 7.X Exercise Set: 1 - 44 ( as many odd numbered as necessary for understanding), 47 - 76 ( as many odd numbered as necessary for understanding)

 

Section 7.5: Rationalizing Denominators and Numerators of Radical Expressions

Textbook Objectives
  1. Simplify complex fractions by simplifying both numerator and denominator and then dividing.
Additional Goals
  1. Recognize a complex fraction as an indication of ordinary division.

Exponents: Powers, Products, and Quotients

About Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page XXX.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check:
Section 7.X Exercise Set:

 

Section 7.6: Radical Equations and Problem Solving

Textbook Objectives
  1. Simplify complex fractions by simplifying both numerator and denominator and then dividing.
Additional Goals
  1. Recognize a complex fraction as an indication of ordinary division.

 

RADICAL EQUATIONS

Equations: Radical Equations in One Variable

  Illustration

 

Minimal List of Exercises Page XXX.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check:
Section 7.X Exercise Set:

 

Section 7.7: Complex Numbers

Textbook Objectives
  1. Write square roots of negative numbers in the form bi.
  2. Add or subtract complex numbers.
  3. Multiply complex numbers.
  4. Divide complex numbers.
  5. Raise i to powers
Additional Goals
  1. Know the definition of complex number.
  2. Know the definition of real part of a complex number.
  3. Know the definition of complex part of a complex number.
  4. Know the definition of sum of complex numbers.
  5. Know the definition of opposite of a complex number.
  6. Know the definition of difference of two complex numbers.
  7. Know the definition of product of complex numbers.
  8. Know the definition of conjugate of a complex number.
  9. Know the definition of norm of a complex number.
  10. Know the definition of multiplicative inverse of a complex number.
  11. Know the definition of quotient of two complex numbers.

Exponents: Powers, Products, and Quotients

Minimal List of Exercises Page XXX.

If you understand the previous material you should be able to answer the following questions.
Each of the individually listed exercises should be done. In each of the lists (like 5 - 12) work as many as needed to insure that you understand the concept being illustrated or utilized. Most of these questions or question types are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.

Vocabulary and Concept Check:
Section 7.X Exercise Set: