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Roots, Radicals, and Complex Numbers

Chapter 7. Roots, Radicals, and Complex Numbers. Chapter Sections. 7.1 – Roots and Radicals 7.2 – Rational Exponents 7.3 – Simplifying Radicals 7.4 – Adding, Subtracting, and Multiplying Radicals 7.5 – Dividing Radicals 7.6 – Solving Radical Equations 7.7 – C omplex Numbers.

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Roots, Radicals, and Complex Numbers

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  1. Chapter 7 Roots, Radicals, and Complex Numbers

  2. Chapter Sections 7.1 – Roots and Radicals 7.2 – Rational Exponents 7.3 – Simplifying Radicals 7.4 – Adding, Subtracting, and Multiplying Radicals 7.5 – Dividing Radicals 7.6 – Solving Radical Equations 7.7 – Complex Numbers

  3. Roots and Radicals § 7.1

  4. Definitions The symbol √ is called the radical sign and is present in all radical expressions. The expression under the radical sign is called the radicand. The number directly to the left of the radical sign is called the index and gives us the “root” of the expression.

  5. Find Square Roots A squarerootis a radical expression that has an index of 2. The index of a square root is generally not written. Thus, Square Roots • For any positive real number a, • The principal or positive square root of a, written , is the positive number b such that b2 = a. • The negative square root of a, written - , is the opposite of the principal square root of a.

  6. Find Square Roots In this book, whenever we use the words “square root” , we are referring to the principal or positive square root. Note: The square root of a negative number is not a real number. There is no number multiplied by itself that will give you –25.

  7. Finding Square Roots ExampleFor each function, find the indicated value(s).

  8. Find Cube Roots Cube Root The cube root of a number a, written , is the number b such that b3 = a. Examples

  9. Find Cube Roots ExampleFor each function, find the indicated value(s).

  10. Understand Odd and Even Roots Even Root The nth root of a, written , where n is an even index and a is a nonnegative real number, is called an even root and is the nonnegative real number b such that bn = a. Examples

  11. Understand Odd and Even Roots Odd Root The nth root of a, , where n is an odd index and a is any real number, is called an odd root and is the real number b such that bn = a. Examples

  12. Understand Odd and Even Roots Example Indicate whether or not each radical expression is a real number. If the expression is a real number, find its value.

  13. Evaluate Radicals Using Absolute Value Radicals and Absolute Value For any real number a, Examples

  14. Evaluate Radicals Using Absolute Value Example Use the absolute value to evaluate.

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