9-3 Multiply and Divide Radical Expressions
Name
Date
Multiply: ⫺3 5a (2 3 a 2 )(⫺4 8a )
⫺3(2)(⫺4) 5a • 3 a 2 • 8a
24 5 a • 3 a 2 • 8 a
24
120 a 4
24 4 a 4 • 30
24 4 a 4 • 30
24(2a2)
30
48a2 30
Use the
Commutative
and Associative
Properties of Equality.
Simplify: 7
6
Think
a
a
b ⫽ b , where a ⱖ 0 and b ⬎ 0.
So 7 ⫽ 7
6
6
Use the Product
Property of Square Roots.
Multiply.
Factor out perfect
squares.
Use the Product Property
of Square Roots.
6
6
⫽
7•
6
⫽
42
36
Simplify.
⫽ 42
6
Simplify.
Multiply by 1
6
in the form of 6 .
Simplify.
Simplify.
Check students’ work. Steps may vary.
Simplify each radical expression. Assume that all variables represent nonnegative numbers.
Copyright © by William H. Sadlier, Inc. All rights reserved.
1. 3 8 • 2 5 • 4 6
3(2)(4) 8 • 5 • 6
2. 2 12 • 4 7 • 5 15
24 8( 5 )( 6 )
24 240
24 16(15 )
24 16 • 15
24(4) 15
2(4)(5) 12 • 7 • 15
40 1260
40 36( 35 )
40(6) 35
96 15
240 35
4. ⫺2 3 y 2 • 5y 8 • 9 14
5. ⫺3 3x (2 5x ⫹ 6 6 x)
3. –5x 2 • 6 10 • 3 6 x 2
5x(6)(3) 2 • 10 • 6 x 2
90x 120 x 2
90x 4 x 2 ( 30 )
180x2 30
6. ⫺2 2a (3 12a ⫹ 8 5a )
2(5y)(9) 3 y 2 • 8 • 14
90y 366 y 2
90y 16 y 2 ( 21)
360y2 21
7. ( 3 ⫹ 4 7)(5 3 ⫺ 2 7)
5(3) 2 21 20 21 8(7)
15 56 18 21
41 18 21
6 15 x 2 18 18 x 2
6x 15 18x 9 • 2
6x 15 54x 2
8. ( 5⫹ 3 3)(2 5 ⫺ 4 3)
2(5) 4 15 6 15 12(3)
10 36 2 15
26 2 15
Lesson 9-3, pages 230–233.
6 24 a2 16 10 a2
6a 4 • 6 16a 10
12a 6 16a 10
9. (7 2 ⫺ x 5)2
(7 2 x 5 )(7 2 x 5)
49(2) 7x 10 7x 10 5x2
98 14x 10 5x2
5x2 14x 10 98
Chapter 9
225
For More Practice Go To:
Simplify each radical expression. Assume that all variables represent
nonnegative numbers.
10. 5
11. 11
12. 24
7
3
8
7a
14. 8
15.
5b
3
27 • 3
5b 3
81
5b 3
9
7a
2
8 • 2
7a 2
16
7a 2
4
18. 67x
5b
27
5a
19. 11
6x • 7
7
7
42 x
7
5 a • 11
11
11
55 a
11
22. Geometry The length of a side of a square is
3 8 ⫹ 6. What is the area of the square?
(Hint: Area ⫽ s2)
Let s a side of the square
s2 (3 8 6)2 (3 8 6)(3 8 6)
9 64 18 8 18 8 36
9(8) 36 36 8 108 36 8
108 36 4 • 2 108 72 2
The area is 108 72 2 square units.
24 24
8
8
42 42
7
7
3
6
16. 12
5
17. 20
7
12 • 5
5
5
60 ; 4 • 15
5
5
2 15
5
20 • 7
7
7
140 ; 4 • 35
7
7
2 35
7
20. 2 2 a ⫹ 4 a
8a
21. 5 b ⫹ 10 b
5b
2 2a 4 a • 2a
8a
2a
2 4 a2 4 2 a2
5 5 b2 10 5 b2
16 a2
4a4a 2
4a
25 b2
5 b 5 10 b 5
5b
1
3 5
2
23. Geometry The base of a triangle is 5 2 ⫹ 3
and the height is 5 2 ⫺ 3. What is the area
1
of the triangle? (Hint: Area ⫽ 2 bh)
1
1
bh (5 2 3)(5 2 3)
2
2
47
1
1
23.5
(25(2) 3) (47) 2
2
2
The area is 23.5 square units.
24. Simplify: 3 2 ⫹ 6
2 5 ⫹3
(Hint: Multiply both numerator and denominator by 2 5 ⫺ 3 .)
6 10 9 2 12 5 18
3 2 6 2 5 3
6 10 9 2 12 5 18
•
4( 5 ) 9
2 5 3 2 5 3
4 25 6 5 6 5 9
6 10 9 2 12 5 18 .
11
226
Chapter 9
5 b 10 b • 5 b
5b
5b
Copyright © by William H. Sadlier, Inc. All rights reserved.
11
7
•
7
7
77
49
77
7
5
3
•
3
3
15
9
15
3
13. 42
7