Simplifying Radical Expressions

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 07:15 PM UTC

OBJECTIVE:
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.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.3 - 1

2. Chapter 9
Roots, Radicals, and Root
Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.3 - 2

3. 9.3
Simplifying Radical
Expressions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.3 - 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 - 4

5. 9.3 Simplifying Radical Expressions
Use the Product Rule for Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 5

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 - 6

9. 9.3 Simplifying Radical Expressions
Simplifying Radicals
Be careful to leave the
5 inside the radical.
Cannot be simplified further.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 9

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 - 10

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 - 11

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 - 12

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).
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 15

16. 9.3 Simplifying Radical Expressions
The Distance Formula
This is the same answer
we obtained using the
Pythagorean formula.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 9.3 - 16

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