1. Roots, Radicals, and Root Functions7
Chapter
Roots, Radicals, and Root Functions

2. Radical Expressions and Graphs
7.1
Radical Expressions and Graphs
1. Find roots of numbers. 2. Find principal roots. 3. Graph functions defined by radical expressions. 4. Find nth roots of nth powers. 5. Use a calculator to find roots.

3. Objective 1
Find roots of numbers.

4. Find roots of numbers.

5. Simplifying Higher Roots
Classroom Example 1
Simplifying Higher Roots
Find each root. a. b. c.
= 3, because 33 = 27
= 6, because 63 = 216
= 4, because 44 = 256

6. Simplifying Higher Roots (cont.)
Classroom Example 1
Simplifying Higher Roots (cont.)
Find each root. d. e. f.
= 3, because 35 = 243
= 0.4, because 0.43 = 0.064

7. Objective 2
Find principal roots.

8. Find principal roots.

9. Finding Roots Find each root. a. b. c. d. = 6 = 3 = –6 = –3 = 2 = –2
Classroom Example 2
Finding Roots
Find each root. a. b. c. d.
= 6
= 3
= –6
= –3
= 2
= –2
Not a real number

10. Graph functions defined by radical expressions.
Objective 3
Graph functions defined by radical expressions.

11. Graph functions defined by radical expressions.
A radical expression is an algebraic expression that contains radicals. Square Root Function

12. Graph functions defined by radical expressions.
Cube Root Function

13. Graphing Functions Defined with Radicals
Classroom Example 3
Graphing Functions Defined with Radicals
Graph each function, and give its domain and range. a. Create a table of values. x y –2 –1 1
1.41 2

14. Graphing Functions Defined with Radicals (cont.)
Classroom Example 3
Graphing Functions Defined with Radicals (cont.)
Graph each function, and give its domain and range. b. Create a table of values. x y –3
–1.587 –1 1 2

15. Find nth roots of nth powers.
Objective 4
Find nth roots of nth powers.

16. Find nth roots of nth powers.

17. Simplifying Square Roots Using Absolute Value
Classroom Example 4
Simplifying Square Roots Using Absolute Value
Find each square root. a. b. c. d.

18. Find nth roots of nth powers.

19. Simplifying Higher Roots Using Absolute Value
Classroom Example 5
Simplifying Higher Roots Using Absolute Value
Find each root. a. b. c. d.

20. Use a calculator to find roots.
Objective 5
Use a calculator to find roots.

21. Finding Approximations for Roots
Classroom Example 6
Finding Approximations for Roots
Use a calculator to approximate each radical to three decimal places. a. b. c. d.
≈ 4.123
≈ –19.026 ≈
≈ 9.089

22. Using Roots to Calculate Resonant Frequency
Classroom Example 7
Using Roots to Calculate Resonant Frequency
In electronics, the resonant frequency f of a circuit may be found using the formula shown below, where f is the cycles per second, L is in henrys, and C is in farads. (Henrys and farads are units of measure in electronics.) Find the resonant frequency f if L = 6  10–5 and C = 4  10–9, to the nearest thousand.