Name: ________________________ Class: ___________________ Date: __________
ID: A
Chapter 2 Practice Test - Non Calculator Section. Powers and Roots
Short Answer
1. Evaluate
2. Evaluate
4
4096 .
3
−64 .
3. Write an equivalent form of
4. Evaluate
6
as a square root.
11
0.0289 .
5. Estimate the value of
3
30 to one decimal place.
6. Which of these numbers is rational?
4
,
169
8,
3
25 ,
8.1
7. Between which two consecutive integers on a number line would you locate
1
3
−3 ?
Name: ________________________
ID: A
8. Which of these numbers is an integer, but not a whole number?
–7, 0, 2, 6
9. Which of these numbers is a natural number?
2, 0, –1, 5.1
10. Which of these numbers is a whole number, but not a natural number?
0, –3, 1, 3.7
11. To which set(s) of numbers does −
200 in simplest form.
12. Write
13. Write
9 belong?
4
162 in simplest form.
14. Write 9 2 as an entire radical.
2
Name: ________________________
ID: A
15. Write 2 3 25 as an entire radical.
16. Write 6 35 as an entire radical.
17. A square has an area of 360 square inches. Determine the side length of the square as a radical in simplest
form.
1
3
18. Evaluate 64 without using a calculator.
1
2
19. Evaluate 0.25 without using a calculator.
20. Evaluate −27
1
3
1296
21. Evaluate
625
without using a calculator.
1
4
without using a calculator.
5
4
22. Write 43 as a radical.
3
Name: ________________________
23. Write
5
2
ID: A
5
as a power.
5
4
24. Evaluate 0.0256 .
0.4
25. Evaluate −3125
.
26. Write 7.5 1.75 as a radical.
27
27. Evaluate
216
4
3
243
28. Evaluate −
1024
.
1.2
.
29. Evaluate 7 −3 without using a calculator.
30. Evaluate
11
7
−3
.
4
Name: ________________________
31. Evaluate 216
−
4
3
32. Evaluate −216
33. Evaluate 1.44
ID: A
without using a calculator.
−
−
1
3
1
2
without using a calculator.
without using a calculator.
34. Evaluate 16 −0.75 without using a calculator.
35. Simplify
15p 5 q −4
25pq 3
18
. Write using powers with positive exponents.
36. Simplify 125a b
2
5
−
4
3
37. Simplify 7s t
12
2
3
.
−6s
−
9
4
t
7
3
.
5
Name: ________________________
4
38. Simplify
54x y
5
6x 8 y −3
3
4
4
39. Evaluate −
3
ID: A
1
2
.
4
⋅ −
3
5
4
.
5
2
40. Evaluate
0.36
.
0.36 4
41. Write the prime factorization of 1386.
42. Determine the greatest common factor of 72 and 90.
43. Determine the greatest common factor of 72, 96, and 132.
44. Determine the least common multiple of 15 and 18.
45. Determine the least common multiple of 99 and 135.
6
Name: ________________________
ID: A
46. One neighbour cuts his lawn every 4 days. Another neighbour cuts her lawn every 6 days. Suppose both
neighbours cut their lawns today. How many days will pass before both neighbours cut their lawns on the
same day again?
47. Determine the square root of 455 625.
48. Determine the perfect square whole number closest to 6625.
49. Determine the side length of this square.
19 ?
50. Between which 2 consecutive whole numbers is
7
Name: ________________________
51. What is the least whole number greater than
52. Estimate the value of
ID: A
54 ?
46 to the nearest tenth.
53. Find the area of this square.
54. Find
100 .
55. Find 62.
6
56. Find
7
2
.
8
Name: ________________________
57. Find
16
.
81
58. Find
0.36 .
ID: A
59. Evaluate: −3 0
60. Evaluate: −10 1
61. Evaluate
3
−729 .
62. Estimate the value of
3
45 to one decimal place.
63. Which of these numbers are rational numbers, but not integers?
4
1
5.17, –4, 5 , , 3.2, 3 −27 , 0, 4 , 4 16
7
2
64. Write 6 7 as an entire radical.
9
Name: ________________________
4
65. Write
5
66. Write
6
6
7
as a radical.
0.4
7
as a power.
4
3
67. Evaluate −125
68. Evaluate
8
125
69. Evaluate 0.64
70. Evaluate 16
−
ID: A
3
2
−
−
.
4
3
1
2
without using a calculator.
without using a calculator.
without using a calculator.
10
Name: ________________________
3 −4 −8 −2
m n p
71. Simplify
4
72. Evaluate
−
4
17
2
3
⋅ −
ID: A
−3
.
4
17
−
2
3
7
.
73. The number 3689_ has a missing last digit. Determine the smallest digit so that the 5 digit number is divisible
by 4.
74. Which of these numbers is not a perfect square: 16, 17, 49, or 81?
75. Simplify
−4a −3 b −8 c −5
. Write using powers with positive exponents.
16a −8 b −3 c −3
Problem
76. Is the cube root of 40 rational or irrational?
Use 2 different strategies to justify your answer.
11
Name: ________________________
ID: A
77. This diagram shows a cube with volume V cubic units and edge length s units.
Provide a value of V for which s is rational.
78. Is 7.21 a good estimate of
Justify your answer.
52 ?
79. Draw a factor tree to find the factors of 40 that are prime.
12
ID: A
Chapter 2 Practice Test - Non Calculator Section. Powers and Roots
Answer Section
SHORT ANSWER
1. ANS:
8
2. ANS:
–4
3. ANS:
36
121
4. ANS:
0.17
5. ANS:
3.1
6. ANS:
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
4
169
ANS:
–1 and –2
ANS:
–7
ANS:
2
ANS:
0
ANS:
II and III only
ANS:
10 2
ANS:
34 2
ANS:
162
ANS:
3
200
ANS:
1260
ANS:
6 10 in.
ANS:
4
1
ID: A
19. ANS:
0.5
20. ANS:
–3
21. ANS:
6
5
22. ANS:
4
43
5
23. ANS:
5
2
5
2
24. ANS:
0.010 24
25. ANS:
25
26. ANS:
4
7.5 7 , or
4
7.5
7
27. ANS:
81
1296
28. ANS:
729
4096
29. ANS:
1
343
30. ANS:
343
1331
31. ANS:
1
1296
32. ANS:
1
–
6
33. ANS:
5
6
34. ANS:
1
8
2
ID: A
35. ANS:
3p 4
5q 7
36. ANS:
25a 12 b 8
37. ANS:
5
3
42t
s
38. ANS:
3y 4
−
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
x2
ANS:
16
9
ANS:
125
27
ANS:
2 ⋅ 3 2 ⋅ 7 ⋅ 11
ANS:
18
ANS:
12
ANS:
90
ANS:
1485
ANS:
12 days
ANS:
675
ANS:
6561
ANS:
67 cm
ANS:
4 and 5
ANS:
8
ANS:
6.8
ANS:
81 square units
3
ID: A
54. ANS:
10
55. ANS:
36
56. ANS:
36
49
57. ANS:
4
9
58. ANS:
0.6
59. ANS:
–1
60. ANS:
–10
61. ANS:
−9
62. ANS:
3.6
63. ANS:
1
4
5.17, , 3.2, and 4
7
2
64. ANS:
252
65. ANS:
6
4
5
7
or
7
4
5
6
66. ANS:
0.4
7
6
or
4
10
7
6
67. ANS:
625
68. ANS:
625
16
69. ANS:
5
4
70. ANS:
1
64
4
ID: A
71. ANS:
64 12 24 6
m n p
27
72. ANS:
1
73. ANS:
2
74. ANS:
17
75. ANS:
a5
− 5 2
4b c
PROBLEM
76. ANS:
40 is not a perfect cube, so the cube root of 40 is irrational.
3
40 = 3.419 951 893 353. . .
3.419 951 893 353. . . does not appear to terminate or repeat.
So, the cube root of 40 is likely irrational.
77. ANS:
The formula for the volume, V, of a cube with edge length s units is:
V = s3
To determine the value of s, take the cube root of each side.
3
3
3
V = s3
V =s
For s to be rational, V must be a positive number that is a perfect cube.
For example, V = 125
78. ANS:
7.21 × 7.21 = 51.9841 (very close to 52)
Test 7.21:
Test whether another estimate to the nearest hundredth might be closer.
Test 7.2:
7.2 × 7.2 = 51.84 (not as close)
Test 7.22:
7.22 × 7.22 = 52.1284 (not as close)
51.9841 is closest to 52.
So, 7.21 is a good estimate of 52 .
5
ID: A
79. ANS:
Write 40 as a product of 2 factors.
Factor 40 as:
40 = 4 × 10
4 and 10 are composite numbers, so we can factor again.
4=2×2
10 = 5 × 2
So, the factors of 40 that are primes are:
2, 5
6