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Lesson 11-2
Operations With Radical Expressions
Lesson Objectives
1 Simplify sums and differences
2 Simplify products and quotients
NAEP 2005 Strand: Algebra
Topic: Variables, Expressions and Operations
Local Standards: ____________________________________
Vocabulary.
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Like radicals are
Unlike radicals are
Conjugates are
Examples.
1 Combining Like Radicals Simplify 4 !3 !3.
!3 (
!3
!3
) !3
Both terms contain
.
Use the Distributive Property to combine like radicals.
Simplify.
2 Simplifying to Combine Like Radicals Simplify 8 !5 !45.
8 5 8 5 45 8 5 5 (
5
? 5
? 5
5
)5
is a perfect square and a factor of 45.
Use the Multiplication Property of Square Roots.
Simplify
.
Use the Distributive Property to combine like terms.
Simplify.
Quick Check.
1. Simplify each expression.
a. –3 !5 4 !5
198
Algebra 1 Lesson 11-2
b. !10 5!10
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4 !3 !3 Name_____________________________________ Class____________________________ Date ________________
Examples.
3 Using the Distributive Property Simplify !5 !8 9 .
(
5
) ? 5
(
)
5 8 9 Use the Distributive Property.
5
Use the Multiplication Property of Square Roots.
Simplify.
4 Simplifying Using FOIL Simplify !6 3 !21 !6 !21 .
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(
)
(6 321) (6 21)
2
)
(
? 14 ?
14
3
126 3
2
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)(
3
Use FOIL.
Combine like radicals and simplify 36 and 441.
is a perfect-square factor of 126.
63 Use the Multiplication Property of Square Roots.
63
Simplify 9 .
Simplify.
Quick Check.
Simplify each expression.
2. a. 3 !20 2 !5
b. 3 !3 2 !27
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3. a. !5(2 !10 )
b. !2x(!6x 11)
4. a. (2 !6 3 !3)( !6 5 !3)
b. ( !7 4)2
Algebra 1 Lesson 11-2
199
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Example.
5 Art A painting has a length : width ratio approximately equal to the golden ratio
(1 !5) : 2. The length of the painting is 51 in. Find the exact width of the painting
in simplest radical form. Then find the approximate width to the nearest inch.
Relate
(1
5) : 2 length : width
51 length of painting
Define
x width of painting
5)
2
(1 5) x
(
1 5
)
Cross multiply.
102
x
102
1 5
x
Solve for x.
(1
x
Multiply the numerator and denominator by
?
102(1 5)
the
102(1 5)
5)
Divide 102 and 4 by the common factor
Use a calculator.
x Round.
The exact width of the painting is
of the denominator.
Multiply and simplify the denominator.
x
width of the painting is
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(1
.
inches. The approximate
inches.
Quick Check.
5. Another painting has a length : width ratio approximately equal to the golden
ratio (1 !5 ) : 2. Find the length of the painting if the width is 34 inches.
200
Algebra 1 Lesson 11-2
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