1. Roots, Radicals, and Complex Numbers
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
Chapter 1 Outline

3. § 7.1
Roots and Radicals

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 square root is 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
Example For each function, find the indicated value(s).

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

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

10. Understand Odd and Even Roots
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.