Free Printable Roots Review

1.

John is trying to build a square garden with an area of 77 square meters. He is wondering between which two integers (in meters) will the length of one side of his garden fall?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

2.

In between what two integers is the square root of 44?

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

3.

√100

a)

15

b)

10

c)

11

d)

12

4.

John has 16 apples. He wants to distribute them equally among his friends. If each friend gets the square root of 16 apples, how many apples does each friend get?

a)

4

b)

8

c)

2

d)

9

5.

√64

a)

3

b)

8

c)

7

d)

6

6.

Level 2: Which number has a square root that is between 5 and 6?

a)

48

b)

81

c)

28

d)

36

7.

Level 3: Estimate the square root.

a)

Between 4 and 5 and closer to 5

b)

Between 5 and 6 and closer to 6

c)

Between -4 and -5 and closer to -5

d)

Between -5 and -6 and closer to -6

8.

Level 3: Estimate the square root.

a)

Between 3 and 4 and closer to 3

b)

Between 2 and 3 and closer to 3

c)

Between 3 and 4 and closer to 4

d)

Between 2 and 3 and closer to 2

9.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

10.

Level 2

Identify the letter that best estimates the following square root on the following number line.

√156

a)

d

b)

b

c)

c

d)

e

11.

Round to the Nearest Hundredth: √7

a)

3.5

b)

2.7

c)

2.8

d)

14

12.

What is $\sqrt[]{144}$ ?

a)

144

b)

144

c)

12

d)

288

13.

What is $\sqrt[]{36}$ ?

a)

36

b)

6

c)

18

d)

72

14.

The area of a square is 36 cm². What is the length of one side?

a)

6 cm

b)

24 cm

c)

9 cm

d)

9 cm

15.

The area of a square picture frame is 100 cm². What is the perimeter of the frame?

a)

25 cm

b)

10 cm

c)

40 cm

d)

50 cm

16.

If I know the area of a square, how do I find the side length?

a)

I square the area.

b)

I divide the area by 2.

c)

I take the square root of the area.

d)

I divide the area by 4.

17.

x² = 121
What does x equal?

a)

11²

b)

11 and -11

c)

20 and 11

d)

12 and 1

18.

√-9

a)

3

b)

-3

c)

81

d)

Not possible

19.

Evaluate.

a)

7/5

b)

±7/5

c)

5/7

d)

±5/7

20.

∛8

(a)

21.

Evaluate ∛27

(a)

22.

Evaluate ∛64

(a)

23.

Evaluate ∛125

(a)

24.

Evaluate ∛512

(a)

25.

Find the cube root.

a)

-4

b)

4

c)

8

d)

-8

26.

A cube with side length s has a volume of 64 cubic units. What is the length of the side of the cube?

a)

32 units

b)

16 units

c)

8 units

d)

4 units

27.

Find the AREA of this figure.

a)

20 square feet

b)

20 cm

c)

25 square cm

d)

20 cm sq.

28.

The volume of a cube is 1,000 cm³. What is the length of each side of the cube?

a)

1

b)

10

c)

100

d)

300

29.

What number, n, cubed is equal to 64?

n³ = 64

a)

4

b)

2

c)

8

d)

262,144

30.

What is the cube root of 27?

a)

9

b)

3

c)

-3

d)

-9

31.

What number, n, cubed is equal to 64?

n³ = 64

a)

4

b)

2

c)

8

d)

262,144

32.

$y^3=125$
Find the value of y

a)

5

b)

15

c)

20

d)

25

33.

Find the cube root of 729:

a)

9

b)

81

c)

243

34.

A cube with side length s has a volume of 64 cubic units. What is the length of the side of the cube?

a)

32 units

b)

16 units

c)

8 units

d)

4 units

35.

Each side of this ice cube measures 2 inches. What is the volume of the ice cube?

a)

6 cubic inches

b)

8 cubic inches

c)

12 cubic inches

d)

8 square inches

36.

The area of a square painting is 81 $cm^2$ . What is the length of one side?

a)

9

b)

-9

c)

40.5

d)

-40.5

37.

Mr. Woodside is building a garden outside of Walker-Grant Middle School. He has enough fertilizer to cover 121 square feet. If Mr. Woodside wants to make a square garden, what should the length of each side be?

a)

12ft

b)

121ft

c)

11ft

d)

13ft

38.

Point B could represent which of the following numbers?

a)

√24

b)

√30

c)

√35

d)

√42

39.

Between which two whole numbers does the √115 fall?

a)

9 and 10

b)

10 and 11

c)

9 and 11

d)

11 and 12

40.

The area of a square is 117 square meters. Which best represents the length of a side of the square?

a)

10.8 m

b)

11 m

c)

10 m

d)

11.2 m

41.

a)

A

b)

B

c)

C

d)

D

42.

Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

43.

a)

a

b)

b

c)

c

d)

d

44.

The ∛24 is closest to which point on the number line?

a)

A

b)

B

c)

C

d)

D

45.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

46.

Estimate √89 to the nearest tenth:

a)

9.4

b)

9.1

c)

9.9

d)

10.1

47.

Estimate √5 to the nearest tenth:

a)

2.2

b)

2.9

c)

4.1

d)

3.2

48.

In between what two integers is the square root of 77?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

49.

If your classroom is built in the shape of a square and has an area of 225 ft², what is the length of one of the sides?

a)

15ft

b)

20ft

c)

25ft

d)

56.25ft

50.

Solve each equation for x:

a)

9

b)

3

c)

6

d)

12

51.

27 is a perfect cube

a)

true

b)

false

52.

$\sqrt{36}=$

a)

4

b)

9

c)

6

d)

12

53.

The volume of a cube is found by _________

a)

$A=l\times w$

b)

$V=s^3$

c)

$A=\frac{1}{2}\times b\times h$

54.

$3\sqrt{64}=$

a)

8

b)

5

c)

4

d)

12

55.

$x^2=100.\ \ What\ does\ x=?$

a)

0

b)

90

c)

1

d)

10

56.

$x^3=1,000.\ \ What\ does\ x=?$

a)

1

b)

100

c)

10

d)

0

57.

Squaring a number means multiplying a number by itself.

a)

True

b)

False

58.

Cubing a number means multiplying a number by itself 3 times.

a)

True

b)

False

59.

Between which two integers is the square root of 20?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

60.

Between which two square roots does the √51 fall?

a)

√16 and √25

b)

√25 and √36

c)

√36 and √49

d)

√49 and √64

61.

Between which two whole numbers does the √22 fall?

a)

3 and 5

b)

3 and 4

c)

4 and 5

d)

5 and 6

62.

How do you write 2 x 2 x 2 x 2 with an exponent?

a)

4²

b)

2⁴

c)

2²

63.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

64.

Simplify (2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

65.

According to exponent rules, when we divide powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

66.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

67.

Write the following in expanded form.
10³

a)

10+10+10

b)

10x10x10

c)

3x10

d)

1,000

68.

Simplify (-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

69.

a)

1³

b)

4³

c)

1^1.6

d)

4^1.6

70.

Solve using the product law of exponents

Resolver utilizando la ley de productos de los exponentes

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

71.

Simplify.

Simplificar.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

72.

Evaluate and leave answer as an exponent.

Evaluar y dejar la respuesta como exponente.

4⁸(4⁸)(4^-5)

a)

64¹¹

b)

4¹¹

c)

64²¹

d)

4^-21

73.

Use the product law to solve.

Utilice la ley de productos para resolver.

(7^-17)(7^-24)

a)

7 ^-7

b)

49⁶⁹⁷

c)

7 ^-41

d)

49 ^-41

74.

x²•x¹⁰

a)

x²⁰

b)

x⁸

c)

x¹²

d)

Choose if you are Guerra

75.

$m^2\cdot m^6\cdot m=$

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

76.

$x^{-3}\cdot x^7\cdot x^2$ =

a)

$x^6$

b)

$x^{12}$

c)

$x^{-42}$

d)

$x^{-12}$

77.

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

a)

Add

b)

Subract

c)

Multiply

d)

Divide

78.

$\frac{x^9}{x^4}$ =

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

79.

$\frac{x^{17}}{x^8}$

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

80.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

81.

$\frac{a^5b^{10}}{a^3b^6}=$

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

$a^{15}b^{60}$

d)

$a^2b^{16}$

Roots Review

Total questions: 81

Worksheet time: 5hrs 8mins

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