Numbers & Operations 8th Grade Chapter Questions
1. What are the properties of a square?
2. What does taking the square root have to do with the area of a square?
3. Why is it helpful to memorize perfect squares?
4. What can be helpful when finding the square roots of numbers greater than 400?
5. Explain how to take the square root of a fraction or a decimal.
6. Explain how to approximate a square root.
7. What is the difference between an irrational and rational number?
8. Explain how to convert between the different forms of a rational number.
Numbers & Operations Chapter Problems
Converting Repeating Decimals to Fractions and Decimal Expansion
Classwork
1. Write each repeating decimal as a fraction in simplest form*
a. 0.7
b. 0.24
c. 5.61
d. 3.5
e. 1.123
f. 6.9
2. Find the decimal expansion of the following*:
a. 415
b. 512
c. 1320
d. 138
e. 325
f. 145
Homework
3. Write each repeating decimal as a fraction in simplest form*
a. 0.43
b. 0.8
c. 2.72
d. 4.36
e. 1.234
f. 3.9
4. Find the decimal expansion of the following[*]:
a. 58
b. 1730
c. 215
d. 524
e. 160
f. 89
Squares, Square Roots & Perfect Squares
Classwork
5. A square has an area of 9 units2.
a. What is the side length of a square of this area?
b. Draw a square with an area of 9 units2.
c. What is the square root of 9?
d. Explain why your answers in parts (a) and (c) are the same.
6. Fill in the following table:
Side Length of a square(units) / Area of the square
(units2)
1
2
3
4
5
6
7
8
9
10
11
12
13
7. Explain how the table above helps you find the square root of 121?
8. Simplify each square root.
a. 25
b. 64
c. 81
d. 49
e. 16
Homework
9. A square has an area of 36 units2.
a. What is the side length of a square of this area?
b. Draw a square with an area of 36 units2.
c. What is the square root of 36?
d. Explain why your answers in parts (a) and (c) are the same.
10. Fill in the following table:
Side Length of a square(units) / Area of the square
(units2)
14
15
16
17
18
19
20
11. Simplify each square root.
a. 289
b. 400
c. 196
d. 361
e. 144
Squares of Numbers Greater Than 20
Classwork
12. Fill in the following table:
Side Length of a square(units) / Area of the square
(units2)
10
20
30
40
50
60
70
80
90
100
13. If you compare that to the table of side lengths from 1-10, what pattern do you notice?
14. Simplify each square root.
a. 2809
b. 7921
c. 484
d. 6400
e. 2025
f. 225
g. 841
h. 9409
i. 961
j. 4356
Homework
15. Simplify each square root.
a. 5041
b. 1296
c. 8464
d. 3025
e. 3721
f. 6889
g. 576
h. 2401
i. 2500
j. 289
Simplifying Perfect Square Radical Expressions
Classwork
16. Simplify each square root.
a. 25
b. 64
c. -81
d. -81
e. 49
f. 2549
g. -16121
h. 36144
i. 2549
j. -25100
k. .64
l. .0081
m. -.25
n. .0016
o. -.04
Homework
17. Simplify each square root.
a. 289
b. -400
c. 64
d. 361
e. -10000
f. 25225
g. -81400
h. -3664
i. 10010000
j. -.09
k. -.0196
l. .49
m. .0361
n. .25
Approximating Square Roots
Classwork
18. What two integers do the following square roots fall between?
a. 68
b. 149
c. 5
d. 52
e. 105
19. Draw and label a number line from 0 to 10. Place the following square roots on the number line.
a. 56
b. 97
c. 11
d. 31
e. 6
20. Estimate the following square roots.
a. 6
b. 70
c. 55
d. 14
e. 106
f. 41
g. 80
h. 65
i. 8
j. 233
21. Approximate the square root to the nearest integer
a.
b.
c.
d.
e.
22. For what integer x is x closest to 7.42?[*]
23. For what integer x is x closest to 5.1?*
24. For what integer x is x closest to 3.9?*
Homework
25. What two integers do the following square roots fall between?
a. 158
b. 12
c. 99
d. 66
e. 175
26. Draw and label a number line from 0 to 10. Place the following square roots on the number line.
a. 39
b. 84
c. 14
d. 21
e. 58
27. Estimate the following square roots.
a. 78
b. 7
c. 63
d. 29
e. 42
f. 138
g. 300
h. 148
i. 21
j. 52
28. Approximate the square root to the nearest integer
a.
b.
c.
d.
e.
29. For what integer x is x closest to 5.2?[*]
30. For what integer x is x closest to 6.1?*
31. For what integer x is x closest to 6.9?*
Rational & Irrational Numbers
Classwork.
32. Circle the numbers below that are rational
a. 3.5
b. 6
c. π
d. 13
e. 10
f. -49
g. 108
h. 0.25
i. 215
j. 0.
[*] From Engage NY
[*] From Engage NY
[*] From Engage NY