9-2 Add and Subtract Radical Expressions
Name
Date
Simplify: ⫺7 2 ⫹ 8 11 ⫹ 16 2 ⫺ 13 11
⫺7 2 ⫹ 8 11 ⫹ 16 2 ⫺ 13 11
Identify like radicands.
(⫺7 2 ⫹ 16 2 ) ⫹ (8 11 ⫺ 13 11)
(⫺7 ⫹ 16) 2 ⫹ (8 ⫺ 13) 11
9 2 ⫺ 5 11
Use the Commutative and Associative Properties of Equality.
Apply the Distributive Property.
These terms have unlike radicands. Do not combine.
Simplify: 11 50 x 2 ⫹ 4x3 8 x 4 ⫺ 7x 28 x 8 ⫺ 3 32 x 2
11 25 x 2 • 2 ⫹ 4x3 4 x 4 • 2 ⫺ 7x 4 x 8 • 7 ⫺ 3 16 x 2 • 2
11 25 x 2 • 2 ⫹ 4x3 4 x 4 • 2 ⫺ 7x 4 x 8 •
7 ⫺ 3 16 x 2 • 2
11(5 | x | 2 ) ⫹ 4x3(2x2 2 ) ⫺ 7x(2x4 7) ⫺ 3(4 | x | 2 )
55|x| 2 ⫹
8x5
2⫺
14x5
7 ⫺ 12|x| 2
8x5 2 ⫺ 14x5 7⫹ (55 | x | 2 ⫺ 12|x| 2 )
8x5
2⫺
14x5
7⫹ (55 | x | ⫺ 12|x|) 2
8x5 2 ⫺ 14x5 7 ⫹ 43 | x |
2
Factor out perfect squares in the
radicand, wherever possible.
Use the Product Property of
Square Roots.
Simplify.
Identify like radicands and like terms.
Use the Commutative Property of Equality.
Apply the Distributive Property.
Simplify.
Simplify each expression. (Hint: a x ⫾ b x ⫽ ( a ⫾ b) x , where a and b ⱖ 0.)
1. 6 7 ⫺ 4 13 ⫹ 9 7 ⫹ 11 13
2. 5 14 ⫺ 2 10 ⫹ 3 14 ⫹ 14 10
(14 10 2 10) (5 14 3 14)
(14 2) 10 (5 3) 14
(6 7 9 7) (4 13 11 13)
(6 9) 7 (4 11) 13
12 10 8 14
15 7 7 13
Copyright © by William H. Sadlier, Inc. All rights reserved.
3. 26 ⫺ 3 21 ⫹ 7 2 ⫹ 18
4. 15 ⫺ 4 30 ⫹ 22 ⫹ 8 3
(26 18) 3 21 7 2
(15 22) 3 30 7 3
44 3 21 7 2
5. 9 12 ⫺ 7 63 ⫹ 8 75 ⫹ 3 28
37 4 30 8 3
6. 5 18 ⫺ 11 125 ⫹ 4 98 ⫹ 2 180
9 4 • 3 7 9 • 7 ) 8 25 • 3 3 4 • 7
18 3 40 3 21 7 6 7
5 9 • 2 11 25 • 5 4 49 • 2 2 36 • 5
15 2 28 2 55 5 12 5
58 3 15 7
7. ⫺9 448 ⫺ 5 1300 ⫹ 8 325 ⫹ 6 700
43 2 43 5
8. ⫺6 405 ⫺ 7 1500 ⫹ 4 735 ⫹ 2 500
9(8) 7 5(10) 13 8(5) 13 6(10) 7
72 7 60 7 50 13 40 13
6(9) 5 7(10) 15 4(7) 15 2(10) 5
54 5 20 5 70 15 28 15
12 7 10 13
9.
2366 ⫹ 1183 ⫺
847 ⫺
686
13 14 7 14 13 7 11 7
6 14 2 7
34 5 42 15
10.
6615 ⫺
6250 ⫹
3840 ⫺
2890
21 15 16 15 25 10 17 10
Lesson 9-2, pages 228–229.
37 15 42 10
Chapter 9
223
For More Practice Go To:
Simplify each expression.
a ⫺7 5
3 a
(3 1)
12. 6 b ⫺ 8 3 ⫹
a 2 5 7 5
a (2 7) 5
6 b b 8 3 11 3
(6 1) b (8 11) 3
4 a9 5
7 b 19 3
13. 2d ⫺ 11 99 ⫺ 5d ⫹ 4 704
14. 8f ⫺ 6 288 ⫺ 17f ⫹ 3 800
2d 5d 11 9 • 11 4 64 • 11
3d 33 11 32 11
8f 17f 6 144 • 2 3 400 • 2
9f 72 2 60 2
3d 11
9f 12 2
15. 9 | n | 17 ⫺ 5 17 n2 ⫹ 11 | n | 272
16. 12|m| 19 ⫺ 6 19 m 2 ⫹ 8 | m | 1216
9 | n | 17 5 | n| 17 11 | n | 16 • 17
4 | n | 17 44 | n | 17
12 | m | 19 6 | m | 19 8 | m | 64 • 19
6 |m| 19 64 |m| 19
48n 17
70m 19
17. 3y2 25 ⫺ 12 | y | 24 y ⫹ 9 | y | 54
18. 11 | x | 36 ⫺ 4x2 63x ⫹ 10 | x | 72 x
15y2 12 | y | 4 • 6 y 9 | y | 9 • 6
15y2
66 | x | 4x2 9 • 7 x 10 | x | 36 • 2 x
66 | x | 12x2 7 x 60 | x | 2 x
24 | y | 6y 27 | y | 6
2
19. 3 189 ⫹ 0.2 450 x 2 ⫹ 8 | x | 128
4
20. 5 1250 ⫹ 0.4 300 a 2 ⫹ 7 | a | 147
2 21 0.2(3 • 5) | x | 2 8 | x | 64 • 2
2 21 3 | x | 2 64 | x | 2
4
625 • 2 4 | a | 3 49 | a | 3
5
2 21 67 | x | 2
20 2 53a 3
21. Geometry The perimeter of a rectangle is
42 2 ⫹ 18 5. If the width of the rectangle is
7 2 ⫹ 3 5, what is the length?
22. Two numbers have a sum of 17 11 and a
difference of 11. What are the numbers?
Reason logically; Let p perimeter, ᐉ length,
w width; p 2ᐉ 2w; Substitute:
42 2 18 5 2ᐉ 2(7 2 3 5)
2w is (7 2 3 5) (7 2 3 5) 14 2 6 5
Solve for 2ᐉ: 2ᐉ 42 2 18 5 (14 2 6 5) 28 2 12 5; Note: Because (14 2 6 5) (14 2 6 5) 28 2 12 5, ᐉ 14 2 6 5
So the length of the rectangle is 14 2 6 5.
23. Which radical expression is equivalent to 4 3x ⫹ 8?
A. 2 12 x ⫹ 16
B.
C.
D. 2 12 x ⫹
224
b ⫺ 11 3
36 x ⫹
Chapter 9
64
36 x ⫹ 16
64
Guess and Test:
9 11 8 11 17 11 and
9 11 8 11 11
The numbers are 9 11 and 8 11.
Copyright © by William H. Sadlier, Inc. All rights reserved.
11. 3 a ⫺ 2 5 ⫹