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OBJECTIVE:
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.
Sec 9.1 - 1
2. Chapter 9
Functions
Sec 9.1 - 2
3. 9.1
Graphs
Sec 9.1 - 3
4. 9.1 Radical Expressions and Graphs
Objectives
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.
5. 9.1 Radical Expressions and Graphs
Find Roots of Numbers
In Section 1.3, we found square roots of positive numbers
such as
and
because 10 • 10 = 100 and 11 • 11 = 121.
6. 9.1 Radical Expressions and Graphs
Find Roots of Numbers
Simplifying Higher Roots
7. 9.1 Radical Expressions and Graphs
Finding Principal Roots
8. 9.1 Radical Expressions and Graphs
Finding Roots
Because the radicand, 25, is positive, there are
two square roots, –5 and 5. The principal root is
5.
Here, we want the negative square root, –5.
The index is even and the radicand is negative,
so this is not a real number.
The index is odd, so the root is –4 since
(–4)3 = –64.
9. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
10. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
11. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions