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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 1
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 2
Roots, Radicals, and Root Functions
Chapter 9
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 9.3 - 3
9.3
Simplifying Radical Expressions
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 4
9.3 Radical Expressions and Graphs
Objectives
1. Use the product rule for radicals.
2. Use the quotient rule for radicals.
3. Simplify radicals.
4. Simplify products and quotients of radicals with different indexes.
5. Use the Pythagorean formula.
6. Use the distance formula.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 5
9.3 Simplifying Radical Expressions
Use the Product Rule for Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 6
9.3 Simplifying Radical Expressions
Use the Product Rule for Radicals
Cannot be simplified using the product rule because the indexes, are different.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 7
9.3 Simplifying Radical Expressions
Use the Quotient Rule for Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 8
9.3 Simplifying Radical Expressions
Simplifying Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 9
9.3 Simplifying Radical Expressions
Simplifying Radicals
Cannot be simplified further.
Be careful to leave the 5 inside the radical.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 10
9.3 Simplifying Radical Expressions
Simplifying Radicals with Variables
Assume all variables represent positive real numbers.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 11
9.3 Simplifying Radical Expressions
Simplifying Radicals with Variables
Assume all variables represent positive real numbers.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 12
9.3 Simplifying Radical Expressions
Simplifying Radicals – Smaller / Different Indices
Assume all variables represent positive real numbers.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 13
9.3 Simplifying Radical Expressions
Pythagorean Formula
The Pythagorean formula relates lengths of the sides of a right triangle.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 14
9.3 Simplifying Radical Expressions
Pythagorean Formula
90º
a9
5
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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).
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 16
9.3 Simplifying Radical Expressions
The Distance Formula
This is the same answer we obtained using the Pythagorean formula.
