chapter 8 section 5 copyright © 2008 pearson education, inc. publishing as pearson addison-wesley
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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley More Simplifying and Operations with Radicals Slide The conditions for which a radical is in simplest form were listed in the previous section. A set of guidelines to use when you are simplifying radical expressions follows:TRANSCRIPT
Chapter Chapter 88Section Section 55
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
More Simplifying and Operations with Radicals
Simplify products of radical expressions.Use conjugates to rationalize denominators of radical expressions.Write radical expressions with quotients in lowest terms.
1
3
2
8.58.5
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
More Simplifying and Operations with Radicals
Slide 8.5 - 3
The conditions for which a radical is in simplest form were listed in the previous section. A set of guidelines touse when you are simplifying radical expressions follows:
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
More Simplifying and Operations with Radicals (cont’d)
Slide 8.5 - 4
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Objective 11
Simplify products of radical expressions.
Slide 8.5 - 5
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EXAMPLE 1AFind each product and simplify.
Solution:
Multiplying Radical Expressions (cont’d)
Slide 8.5 - 6
2 8 20 2 5 3 3 2 2
2 2 2 4 5
2 2 2 4 5
2 2 2 2 5
4 2 5 2
4 2 10
2 3 2 2 2 5 3 3 5 3 2 2
6 11 10 6
11 9 6
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EXAMPLE 1BFind each product and simplify.
Solution:
Multiplying Radical Expressions
Slide 8.5 - 7
2 5 10 2
2 10 2 2 5 10 5 2
20 2 50 10
2 5 2 5 2 10
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Find each product. Assume that x ≥ 0.
EXAMPLE 2
Solution:
Using Special Products with Radicals
Slide 8.5 - 8
25 3 2
4 2 5 22 x
2
25 2 5 3 3 2
24 2 2 4 2 5 5 222 2 2 x x
5 6 5 9
14 6 5
32 40 2 25
57 40 2
4 4 x x
Remember only like radicals can be combined!
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Using a Special Product with Radicals.Example 3 uses the rule for the product of the sum and
difference of two terms,
Slide 8.5 - 9
2 2.x y x y x y
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EXAMPLE 3 Using a Special Product with Radicals
Slide 8.5 - 10
Find each product. Assume that 0.y
Solution: 3 2 3 2 4 4y y
2 23 2
3 4
1
2 24y
16y
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Objective 22
Use conjugates to rationalize denominators of radical expressions.
Slide 8.5 - 11
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
The results in the previous example do not contain radicals. The pairs being multiplied are called conjugates of each other. Conjugates can be used to rationalize the denominators in more complicated quotients, such as
Use conjugates to rationalize denominators of radical expressions.
Slide 8.5 - 12
2 .4 3
To simplify a radical expression, with two terms in the denominator, where at least one of the terms is a square root radical, multiply numerator and denominator by the conjugate of the denominator.
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EXAMPLE 4A Using Conjugates to Rationalize Denominators
Slide 8.5 - 13
Simplify by rationalizing each denominator. Assume that 0.t
32 5
5+32 5
2 52 55 2
3
2
2
3 2 5
2 5
3 2 5
4 5
3 2 5
1
3 2 5
2 5
2 5
5 3
2 5
2 2
2 5 5 6 3 5
2 5
5 5 114 5
5 5 111
5 5 11
11 5 5
Solution:
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EXAMPLE 4BUsing Conjugates to Rationalize Denominators (cont’d)
Slide 8.5 - 14
Simplify by rationalizing each denominator. Assume that 0.t
32 t
232 2
ttt
2
2
3 2
2
t
t
3 2
4
t
t
Solution:
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Objective 33
Slide 8.5 - 15
Write radical expressions with quotients in lowest terms.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
EXAMPLE 5
Write in lowest terms.
Solution:
Writing a Radical Quotient in Lowest Terms
Slide 8.5 - 16
5 3 1510
5 3 3
10
3 32