Free Printable Unit 4: Squares, Square Roots, & Pythagorean Theorem REVIEW

1.

What is the square root of 25?

a)

5

b)

12

c)

3

d)

6

2.

A perfect square is when a whole number is multiplied by itself?

a)

FALSE

b)

TRUE

3.

Which would be the next number in the pattern?
36, 49, 64, 81 __

a)

82

b)

18

c)

64

d)

100

4.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

5.

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.

6.

What is the side length of a square that has an area of 36?

a)

9

b)

18

c)

6

d)

1296

7.

Which of the following in NOT a perfect square?

a)

49

b)

81

c)

111

d)

144

8.

Which of the following is NOT a perfect square?

a)

1

b)

4

c)

100

d)

8

9.

What would be the side length if you used 49 tiles to create a perfect square?

a)

7 tiles

b)

14 tiles

c)

4 tiles wide and 9 tiles long

d)

3.5 tiles

10.

What is the formula for area?

(a)

11.

If Lucy's square garden has a total perimeter of 12ft, how big is the inside (area) part of the garden?

a)

9ft²

b)

3ft²

c)

36ft²

d)

12ft²

12.

$\sqrt{144}$

a)

12

b)

100

c)

11

d)

13

13.

All sides of a square are (a)

14.

You divide the area by 2 to figure out the side of a square.

a)

True

b)

False

15.

Which perfect square is being shown?

a)

6

b)

7

c)

36

d)

49

16.

What is the square root of 25?

a)

5

b)

12

c)

3

d)

6

17.

√ 16

a)

8

b)

3

c)

4

d)

6

18.

What is the proper name for this symbol: √

a)

radicand

b)

radical

c)

cube root

d)

index

19.

11²=

a)

22

b)

44

c)

144

d)

121

20.

A perfect square is a whole number multiplied by itself

a)

FALSE

b)

TRUE

21.

√49

a)

7

b)

7²

c)

14²

d)

14

22.

5²

a)

5

b)

10

c)

15

d)

None of these

23.

0²

a)

2

b)

0

c)

1

d)

None of these

24.

8²

a)

16

b)

8

c)

64²

d)

64

25.

9²

a)

18

b)

81²

c)

81

d)

none of these

26.

√4

a)

2²

b)

4

c)

16

d)

None of these

27.

6²

a)

36

b)

36²

c)

12

d)

12²

28.

√9

a)

3

b)

3²

c)

9

d)

none of these

29.

√100

a)

10²

b)

10

c)

5

d)

100

30.

The square root of 16 is...

a)

8

b)

4

c)

2

d)

3

31.

True or false? 9² is 18

a)

True

b)

False

32.

65

a)

Is a perfect square.

b)

Is not a perfect square.

33.

Which of the following is a perfect square?

a)

24

b)

48

c)

81

d)

110

34.

1- Which number is a perfect square?

a)

a) 32

b)

b) 25

c)

c) 22

d)

D) 24

35.

2- Which number is a perfect square?

a)

a) 0,09

b)

b) 48

c)

c) 99

d)

d) 10

36.

3- Which number is perfect square?

a)

a) 36

b)

b) 39

c)

c) 89

d)

d) 11

37.

4- Which number is a perfect square?

a)

a) 100

b)

b) 110

c)

c) 120

d)

d) 59

38.

5- Which number is perfect square?

a)

a) 124

b)

b) 144

c)

c) 158

d)

d) 164

39.

6-Which number is perfect square?

a)

a) 1

b)

b) 2

c)

c) 5

d)

d) 8

40.

7- Which number is perfect square?

a)

a) 3

b)

b) 16

c)

c) 33

d)

d) 13

41.

8- Which number is perfect square?

a)

a) 0.25

b)

b) 0.20

c)

c) 0.45

d)

d) 0.24

42.

9- Which number is perfect square?

a)

a) 48

b)

b) 49

c)

c) 59

d)

d) 29

43.

10- Which number is perfect square?

a)

a) 81

b)

b) 89

c)

c) 90

d)

d) 88

44.

11- Which number is perfect square?

a)

a) 65

b)

b) 64

c)

c) 66

d)

d) 67

45.

12- Which number is perfect square?

a)

a) 4

b)

b) 44

c)

c) 34

d)

d) 54

46.

13- Which number is perfect square?

a)

a) 121

b)

b) 122

c)

c) 211

d)

d) 131

47.

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

48.

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

49.

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

50.

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

51.

Level 3: Estimate the square root.

a)

Between 7 and 8 and closer to 8

b)

Between 8 and 9 and closer to 9

c)

Between 9 and 10 and closer to 9

d)

Between 9 and 19 and closer to 10

52.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

53.

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

54.

Level 4

Order from least to greatest.

a)

√45, 9, 6, √63

b)

6, √45, √63, 9

c)

6, √45, 9, √63

d)

√45, √63, 6, 9

55.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

56.

Which is the best estimate of the of √3?

a)

1

b)

2

c)

1 ⅔

d)

2 ⅔

57.

Find the best estimate for √18 .
Look at the number line.

a)

4.2

b)

4.4

c)

5.1

d)

4

58.

Level 4: Estimate the square root to the nearest tenth.

a)

1.7

b)

1.6

c)

1.8

d)

1.9

59.

Level 1: 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

60.

Level 1: 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

61.

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

a)

48

b)

81

c)

28

d)

36

62.

Level 2: Which number has a square root that is between 3 and 4?

a)

14

b)

8

c)

17

d)

0

63.

Level 2: Which number has a square root that is between 10 and 11?

a)

10.5

b)

144

c)

99

d)

101

64.

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

65.

Level 2

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

√490

a)

e

b)

f

c)

g

d)

h

66.

Level 2

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

√467

a)

c

b)

a

c)

b

d)

d

67.

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

68.

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

69.

Level 3: Estimate the square root.

a)

Between 7 and 8 and closer to 8

b)

Between 8 and 9 and closer to 9

c)

Between 9 and 10 and closer to 9

d)

Between 9 and 19 and closer to 10

70.

Level 3: Estimate the square root.

a)

Between 1 and 2 and closer to 1

b)

Between 1 and 2 and closer to 2

c)

Between 2 and 3 and closer to 2

d)

Between 2 and 3 and closer to 3

71.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

72.

Level 4: Estimate the square root to the nearest tenth.

a)

1.7

b)

1.6

c)

1.8

d)

1.9

73.

Level 4: Estimate the square root to the nearest tenth.

a)

3.2

b)

3.1

c)

3.4

d)

3.0

74.

Level 4

Order from least to greatest.

a)

√45, 9, 6, √63

b)

6, √45, √63, 9

c)

6, √45, 9, √63

d)

√45, √63, 6, 9

75.

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

76.

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

77.

√100

a)

15

b)

10

c)

11

d)

12

78.

√16

a)

4

b)

8

c)

2

d)

9

79.

√64

a)

3

b)

8

c)

7

d)

6

80.

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

a)

48

b)

81

c)

28

d)

36

81.

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

82.

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

83.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

84.

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

85.

Round to the Nearest Hundredth: √7

a)

3.5

b)

2.7

c)

2.8

d)

14

86.

Round to the Nearest Hundredth: √13

a)

5.6

b)

2.6

c)

3.9

d)

3.6

87.

Round to the Nearest Hundredth: √28

a)

5.6

b)

5.9

c)

5.3

d)

8

88.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

89.

Find the best estimate for √18 .
Look at the number line.

a)

4.2

b)

4.4

c)

5.1

d)

4

90.

The Area of a square wall is 182 square feet. Which measure is the closest to the side length in feet of this wall?

a)

91.0 ft

b)

13.5 ft

c)

54.0 ft

d)

45.5 ft

91.

A square desktop has an area of 324 square inches. What is the length of one side of the desktop?

(a)

92.

You want to carpet a square room that has an area of 144 square feet. What is the length of one side of the room?

(a)

93.

You are going to decorate one wall of your bedroom by putting border along the top. The wall is a square wall with an area of 256 square feet. What is the length of border you need for the top of this on wall?

(a)

94.

To the nearest tenth, what is the square root of 33?

(a)

95.

The area of a square tile is 50 square centimeters. To the nearest tenth of a centimeter, how long is one side of this tile?

(a)

96.

A student solved the equation $x^2$ = 132 to find the length of the diagonal of a square in centimeters. Which measurement is closest to x, the length of the diagonal of this square, in centimeters?

a)

66 cm

b)

44 cm

c)

33 cm

d)

11 cm

97.

Jason's square bedroom has an area of 90 square feet. What is the closest lengths measurement of the side length of Jason's bedroom? (Use 3 decimal places, thousandths place)

(a)

98.

A square place mat has an area of 169 square inches. What is the closest measurement for Sally to know how long each side of the mat is?

(a)

99.

The Dotson family built a square deck with an area of 65 square meters. What is the closest measure of the square deck the Dotson family will build? (Use 2 decimal places, hundredths place)

(a)

100.

To the nearest tenth, what is the square root of 89?

(a)

101.

A rancher divided his land into square sections. One large section has an area of 112 square miles. To the nearest tenth of a mile, what is the the side length of this large section of land?

(a)

102.

Mr. Mason was hired to tile a square-shaped bathroom. Mr. Mason is laying 676 square feet of tile. What is the length of the bathroom?

a)

676 ft

b)

338 ft

c)

169 ft

d)

26 ft

103.

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

104.

The area of the square pool on your vacation was 260 ft². Approximately how long was one side of the pool?

a)

17 ft

b)

18 ft

c)

16 ft

d)

15 ft

105.

Miss Weber wanted to buy the iPod shuffle (back when that was the cool new thing to have). If the area of the iPod was 9 cm², how long was the side of the iPod shuffle?

a)

3 cm

b)

9 cm

c)

3 in

d)

4 cm

106.

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

107.

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.

108.

What is the side length of a square that has an area of 121?

a)

11

b)

60.5

c)

30.25

d)

14641

109.

What is the side length of a square that has an area of 40?

a)

20

b)

10

c)

1600

d)

6.3

110.

If you had a square garden with an area of 16 square feet, what would be the length, in feet, of one side of the garden

a)

8

b)

4

c)

7

d)

16

111.

What is the length of a side of the square shown?

a)

42.25 inches

b)

84.5 inches

c)

13 inches

d)

14 inches

112.

The Pythagorean Theorem is
c² = a² - b²

a)

false

b)

true

113.

Sides a and b are called legs.

a)

true

b)

false

114.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

115.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

6.2

116.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

117.

Find the length of the missing side.

a)

48 in.

b)

52 in.

c)

16 in.

d)

24 in.

118.

Do the segment lengths 15, 12, and 9 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

119.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

120.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

121.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

122.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

123.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

124.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

125.

a= 12, b= 35, c= ? Find c

a)

32

b)

37

c)

19

d)

20

126.

All of the a square plus all of the b square will perfectly fill the c square with nothing left over.

a)

True

b)

False

127.

You can find right triangles when they build houses.

a)

False

b)

True

128.

c= 97, b= 72, a=?

a)

35

b)

75

c)

65

d)

55

129.

What is the name for side c?

a)

head

b)

body

c)

hippopotamus

d)

hypotenuse

130.

Do the lengths form a right triangle? 6, 8, 10

a)

yes

b)

no

131.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

132.

a)

7 ft

b)

5 ft

c)

3 ft

d)

2 ft

133.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

134.

What is the height of the cone?

a)

14 cm

b)

8 cm

c)

12 cm

d)

13.9 cm

135.

if a = 3 feet, b = 8 feet, and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?

a)

8.54 feet

b)

10.44 feet

c)

10 feet

d)

4.12 feet

136.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

137.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

138.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

139.

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

140.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

141.

you ADD a² and c² then take the square root to find b on a right triangle.

a)

true

b)

false

142.

you ADD a² and b² then take the square root to find c on a right triangle.

a)

true

b)

false

143.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

144.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

145.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

146.

a)

The top of the ladder is 8.9 ft from the ground

b)

The top of the ladder is 9.2 ft from the ground

c)

The top of the ladder is 16.5 ft from the ground

d)

The top o the ladder is 14.4 ft from the ground

147.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

148.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

149.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

150.

_{^{Find the missing side}}

a)

√29.2

b)

√400

c)

√20

d)

√10

151.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

152.

a)

7 ft

b)

5 ft

c)

3 ft

d)

2 ft

153.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

154.

What is the height of the cone?

a)

14 cm

b)

8 cm

c)

12 cm

d)

13.9 cm

155.

if a = 3 feet, b = 8 feet, and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?

a)

8.54 feet

b)

10.44 feet

c)

10 feet

d)

4.12 feet

156.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

157.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

158.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

159.

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

160.

The Pythagorean Theorem is
a² + b³= c⁴

a)

false

b)

true

161.

you ADD a² and c² then take the square root to find b on a right triangle.

a)

true

b)

false

162.

you ADD a² and b² then take the square root to find c on a right triangle.

a)

true

b)

false

163.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

164.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

165.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

166.

a)

The top of the ladder is 8.9 ft from the ground

b)

The top of the ladder is 9.2 ft from the ground

c)

The top of the ladder is 16.5 ft from the ground

d)

The top o the ladder is 14.4 ft from the ground

167.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

168.

Which set of side lengths does not form a right triangle?

a)

38, 80, 90

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

169.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

170.

_{^{Find the missing side}}

a)

√29.2

b)

√400

c)

√20

d)

√10

171.

The Pythagorean Theorem is
c² = a² - b²

a)

false

b)

true

172.

Sides a and b are called legs.

a)

true

b)

false

173.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

6.2

174.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

175.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

176.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

177.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

178.

Which of the following sentences would belong in the proof that describes this image?

a)

The sum of the areas of the two smaller squares is equal to the area of the large square.

b)

The sum of the side lengths of the two smaller squares is equal to the side length of the large square.

c)

The difference of the areas of the two smaller squares is equal to the area of the large square.

d)

The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

179.

Challenge! Find the perimeter of a triangle that has legs that are 3 cm and 4 cm.

a)

5

b)

7

c)

10

d)

12

180.

Find the value of x.

a)

7

b)

8

c)

9

d)

10

181.

What is the opposite of squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

182.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

183.

solve for c

a)

7

b)

9

c)

4

d)

13

184.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

185.

Two LEGS are 9 and 12. What is the hypotenuse?

a)

14

b)

15

c)

17

d)

18

186.

The leg of a triangle is 24 and its hypotenuse is 25. What is the length of its other leg?

a)

5

b)

12

c)

8

d)

7

187.

A right triangle has a hypotenuse of 25 and a leg of 15. What is the length of the other leg?

a)

20

b)

10

c)

12

d)

16

188.

Two legs of a right triangle are 20 and 21. What is the hypotenuse?

a)

28

b)

29

c)

30

d)

27

189.

If the hypotenuse of a right triangle is 50 and the leg is 14, what is the length of the other leg?

a)

48

b)

46

c)

45

d)

42

190.

Will the sides 36, 85 and 77 make a right triangle?

a)

yes

b)

no

191.

What is an example of squaring a number?

a)

2 x 8

b)

5 x 6

c)

5 + 5

d)

7 x 7

192.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

30 cm²

b)

15 cm²

c)

315 cm²

d)

45 cm²

193.

Using the Pythagorean Theorem, find the area of the missing square (seen in picture)

a)

75 cm²

b)

105 cm²

c)

135 cm²

d)

30 cm²

194.

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

a)

12.12

b)

21.2

c)

7.3

195.

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

a)

23

b)

17

c)

7

Unit 4: Squares, Square Roots, & Pythagorean Theorem REVIEW

Total questions: 195

Worksheet time: 23hrs 3mins

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