chapter 8
DESCRIPTION
Chapter 8. Section 4. Rationalizing the Denominator. Rationalize denominators with square roots. Write radicals in simplified form. Rationalize denominators with cube roots. 8.4. 2. 3. Objective 1. Rationalize denominators with square roots. Slide 8.4-3. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 8 Section 4
Objectives
1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Rationalizing the Denominator
Rationalize denominators with square roots.
Write radicals in simplified form.
Rationalize denominators with cube roots.
8.4
2
3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Rationalize denominators with square roots.
Slide 8.4-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Rationalize denominators with square roots.
It is easier to work with a radical expression if the denominators do not contain any radicals.
1 1 222 2
22
2 .2
This process of changing the denominator from a radical, or irrational number, to a rational number is called rationalizing the denominator.The value of the radical expression is not changed; only the form is changed, because the expression has been multiplied by 1 in the form of
Slide 8.4-4
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Rationalize each denominator.
Solution:
1824
6182 6 6
18 62 6
18 612
168
2162 2 2
16 22 2
16 24
4 2
3 62
Slide 8.4-5
EXAMPLE 1 Rationalizing Denominators
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 2
Write radicals in simplified form.
Slide 8.4-6
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Write radicals in simplified form.
Conditions for Simplified Form of a Radical
1. The radicand contains no factor (except 1) that is a perfect square (in dealing with square roots), a perfect cube (in dealing with cube roots), and so on.
2. The radicand has no fractions.
3. No denominator contains a radical.
Slide 8.4-7
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:
5 .18
518
8
518
181
5 1818
5 9 2
18
5 9 2
18
3 5 218
3 1018
106
Slide 8.4-8
EXAMPLE 2 Simplifying a Radical
Simplify
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify
Solution:
1 5.2 6
1 52 6
5
12
512
35
2 3 3
5 36
156
Slide 8.4-9
EXAMPLE 3 Simplifying a Product of Radicals
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify. Assume that p and q are positive numbers.
Solution:
5pq
5 qpq q
5pqq
Slide 8.4-10
EXAMPLE 4 Simplifying Quotients Involving Radicals
357
pq
2 2357p q
2 257
77
p q
2 2 357
p q
2 257p q
2 257p q
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 3
Rationalize denominators with cube roots.
Slide 8.4-11
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Rationalize each denominator.
Solution:
35 6
3
3
23
3
3
3 , 04x
x
2
3
3
23
3 656 6
3 2
3 3
5 6
6
3 1806
2
3
3
23
3 323 3
3 2
3 3
2 3
3
3 183
3 2 2
3 23 2
3 4
4
34
xx x
3 2
3 3 3
3 16
4
x
x
23 3 2 84x
x
3 23 8 6
4x
x
3 262xx
Slide 8.4-12
EXAMPLE 5 Rationalizing Denominators with Cube Roots