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UNDERSTAND PRACTICE
Additional Exercises Available Online
Practice Tutorial
PRACTICE & PROBLEM SOLVING
What is the reduced radical form of each expression? SEE EXAMPLE 1
19. ( 3x 1 __ 2 ) ( 4x
2 __ 3 ) 20. 2b
1 __ 2 ( 3b
1 __ 2 c
1 __ 3 )
2
21. ( x 1 __ 2 ∙ x
5 __ 12
)
4
÷ x 2 __ 3 22. ( 16c 14 ______
81d 18 )
1 __ 2
What is the reduced radical form of each expression? SEE EXAMPLE 2
23. 3 √ ________
250y 2 z 4 24. 4 √ __________
256v 7 w 12
25. √
______
48x 3 ______ 3xy 2
26. √
______
56x 5 y 5
______ 7xy
27. 3 √ ______
216m 28. 3 √
________
250f 7 g 3
_______ 2f 2 g
What is the reduced radical form of each expression? SEE EXAMPLE 3
29. √ _____
x 5 y 5 ∙ 3 √ ______
2 x 7 y 6 30. 3 √ _____
18n 2 ____ 24n
31. 3 √ ____
3x 2 ∙ 3 √ ___
x 2 ∙ 3 √ ____
9 x 3 32. √ _____
162a _____ 6a 3
33. 5 √ _____
2pq 6 ∙ 2 √ _____
2 p 3 q 34. 3 √
___
x 2 ___ 9y
35. 3 √ __
6 ∙ 3 √ ___
16 36. 4 √ ___
2 ___ 5x
What is the reduced radical form of each expression? SEE EXAMPLE 4
37. 4 3 √ ___
81 − 2 3 √ ___
72 − 3 √ ___
24 38. 6 √ _____
45y 2 − 4 √ _____
20y 2
39. 3 √ ___
12 − √ ___
54 + 7 √ ___
75 40. √ ____
32ℎ + 4 √ ____
98ℎ − 3 √ ____
50ℎ
Multiply. SEE EXAMPLE 5
41. (3 √ __
p − √ __
5 )( √ __
p + 5 √ __
5 ) 42. (4m − √ __
3 )(4m − √ __
3 )
43. (3 √ __
2 + 8)(3 √ __
2 − 8) 44. 3 √ __
3 (5 3 √ __
9 − 4)
What is the reduced radical form of each expression? SEE EXAMPLE 6
45. 4 ______ 1 − √
__ 3 46. 20 ______
3 + √ __
2
47. 3 + √ __
8 ______ 2 − 2 √
__ 8 48. −2x ______
3 + √ __
x
13. Model With Mathematics In the expression PV 4 __ 3 ,
P represents the pressure and V represents the volume of a sample of a gas. Evaluate the expression for P = 7 and V = 8 .
14. Reason Describe the possible values of k such that √
___ 32 + √
__ k can be rewritten as a single
term.
15. Error Analysis Explain why the following work is incorrect. Find the correct answer.
✗
12
125 4 – 5 = 5(4) – 5 5
= 15
12= 20 – 25
16. Communicate Precisely Discuss the advantages and disadvantages of first rewriting √
___ 27 + √
___ 48 + √
____ 147 in order to estimate its
decimal value.
17. Higher Order Thinking Write √ __
4 __ 5 in two different ways, one where the numerator is simplified and another where the denominator is rationalized.
18. Construct Arguments Justify each step used in simplifying the expression below.
=
=14a
= √a
=
153
4a2–
34
15
a2
a155
4a
4
LESSON 5-2 Properties of Exponents and Radicals 253
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PRACTICE & PROBLEM SOLVING
APPLY ASSESSMENT PRACTICE
Mixed Review Available Online
Practice Tutorial
49. Model With Mathematics A triangular swimming area is marked off by a rope.
a. If a woman swims around the perimeter of the swimming area, how far will she swim?
b. What is the area of the roped off section?
200 6 m √ 400 m
200 m 200 3 m √
200 3 m
√
50. Use Structure The interest rate r required to increase your investment p to the amount a
in m months is found by r = ( a __ p ) 1 __ m
− 1. What interest rate would be required to increase
your investment of $3,600 to $6,400 over 7 months? Round your answer to the nearest tenth of a percent.
51. Use Structure The length of a rectangle is (2 + √
__ 5 )y . The width is (4 + 3 √
__ 5 )z . What is the
area of the rectangle?
(2+√5 )y(4+3√5 )z
52. Model With Mathematics A rectangular boardroom table is √
____ 440 ft by √
___ 20 ft. Find its
area.
53. Aaron is rewriting 1 + √ __
3 ______ 5 − √
__ 3 into reduced radical
form. Determine if Aaron would have written the steps below to show his work. Select Yes or No.
Yes No
❑
❑
❑
❑❑
❑
❑
❑
❑ ❑
6 + 4√3 – 325 + 9
5 + 6√3 + 325 – 3
5 + √3 + 5√3 +√925 + 5√3 – 5√3 –√94 + 3√3
11
8 + 6√328
54. SAT/ACT Which expression cannot be rewritten as −10?
Ⓐ √ ___
25 ∙ 3 √ ___
−8 Ⓑ 3 √ _____
−125 ∙ 4 √ ___
16
Ⓒ − 3 √ _____
1,000 Ⓓ − √ ___
25 ∙ 5 √ ____
−32
Ⓔ √ __
4 ∙ − 3 √ ____
125
55. Performance Task The volume of a sphere of radius r is V = 4 __
3 πr 3 .
Part A Use the formula to find r in terms of V. Rationalize the denominator.
Part B A snowman is made using three spherical snowballs. The top snowball for the head has a volume of 500 in. 3 . What is the diameter of the top snowball?
V = 1,000 in.3
V = 750 in.3
V = 500 in.3
Part C The volumes of the other two snowballs are 750 in. 3 and 1,000 in. 3 . How tall is the snowman?
254 TOPIC 5 Rational Exponents and Radical Functions Go Online | PearsonRealize.com
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