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

3. Simplifying Radical Expressions
9.3
Simplifying Radical Expressions

4. 9.3 Radical Expressions and Graphs
Objectives
Use the product rule for radicals.
Use the quotient rule for radicals.
Simplify radicals.
Simplify products and quotients of radicals with different indexes.
Use the Pythagorean formula.
Use the distance formula.
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5. 9.3 Simplifying Radical Expressions
Use the Product Rule for Radicals
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6. 9.3 Simplifying Radical Expressions
Use the Product Rule for Radicals
Cannot be simplified using the product rule because the indexes, are different.
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7. 9.3 Simplifying Radical Expressions
Use the Quotient Rule for Radicals
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8. 9.3 Simplifying Radical Expressions
Simplifying Radicals
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9. 9.3 Simplifying Radical Expressions
Simplifying Radicals
Be careful to leave the 5 inside the radical.
Cannot be simplified further.
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10. 9.3 Simplifying Radical Expressions
Simplifying Radicals with Variables
Assume all variables represent positive real numbers.
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11. 9.3 Simplifying Radical Expressions
Simplifying Radicals with Variables
Assume all variables represent positive real numbers.
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12. 9.3 Simplifying Radical Expressions
Simplifying Radicals – Smaller / Different Indices
Assume all variables represent positive real numbers.
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13. 9.3 Simplifying Radical Expressions
Pythagorean Formula
The Pythagorean formula relates lengths of the sides of a right triangle.
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14. 9.3 Simplifying Radical Expressions
Pythagorean Formula 9 a
90º 5
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15. 9.3 Simplifying Radical Expressions
The Distance Formula
The distance formula, which allows us to compute the distance between two points in the coordinate plane is derived from the Pythagorean formula. Find the distance between (1, 6) and (4, –2).
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16. 9.3 Simplifying Radical Expressions
The Distance Formula
This is the same answer we obtained using the Pythagorean formula.
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