2. Roots, Radicals, and Root Functions
Chapter 9
Roots, Radicals, and Root Functions

3. Radical Expressions and Graphs
9.1
Radical Expressions and Graphs

4. 9.1 Radical Expressions and Graphs
Objectives
Find roots of numbers.
Find principal roots.
Graph functions defined by radical expressions.
Find nth roots of nth powers.
Use a calculator to find roots.
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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.
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6. 9.1 Radical Expressions and Graphs
Find Roots of Numbers
Simplifying Higher Roots
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7. 9.1 Radical Expressions and Graphs
Finding Principal Roots
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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.
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9. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
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10. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
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11. 9.1 Radical Expressions and Graphs
Graphs of Functions Defined by Radical Expressions
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12. 9.1 Radical Expressions and Graphs
Simplifying Square Roots Using Absolute Value
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13. 9.1 Radical Expressions and Graphs
Simplifying Higher Roots Using Absolute Value
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14. 9.1 Radical Expressions and Graphs
Use a Calculator to Find Roots
Examples:
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15. 9.1 Radical Expressions and Graphs
Using a Calculator to Find the Velocity of an Orbiting Body
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