Free Printable MIDTERM - Squares, Roots & Pythagorean Theorem

1.

$12^2$

a)

12

b)

2

c)

132

d)

144

2.

$2^3$

a)

6

b)

8

c)

12

d)

3

3.

$\sqrt{100}$

a)

1.0

b)

100

c)

6

d)

10

4.

$\sqrt{25}$

a)

4

b)

6

c)

5

d)

25

5.

$\sqrt{16}$

a)

4

b)

6

c)

16

d)

21

6.

To which shape(s) does the Pythagorean theorem apply?

a)

All triangles

b)

Right triangles only

c)

Some right triangles and some isosceles triangles

d)

Right triangles and circles.

7.

The longest side of a right triangle is called the...

a)

leg A

b)

leg B

c)

hypotenuse

d)

right angle

8.

The longest side of a right triangle is DIRECTLY ACROSS from the...

a)

right angle.

b)

acute angle.

c)

obtuse angle.

9.

The Pythagorean theorem states that:

a)

The two smaller sides of a right triangle sum to equal the longest side.

b)

The squares of the two smaller sides of a right triangle sum to equal the square of the longest side.

10.

If a² = 10 and b² = 30, what is c²?

a)

20

b)

40

c)

300

d)

90

11.

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

a)

Divide both sides by 2

b)

Take the square root of both sides

12.

The Pythagorean Theorem is
a² + b²+ c²

a)

false

b)

true

13.

solve for x

a)

5552363959656.

b)

10

c)

100

d)

89

14.

What is the formula for finding the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

15.

What is

\sqrt{\frac{36}{64}}

a)

$\frac{9}{16}$

b)

$\frac{6}{8}$

c)

$\frac{18}{32}$

d)

is not a perfect square

16.

What is

\sqrt{2.56}

a)

$\frac{64}{10}$

b)

$\frac{4}{5}$

c)

$\frac{16}{10}$

d)

is not a perfect square

17.

Which one is a perfect square number?

a)

$\sqrt{0.12}$

b)

$\sqrt{\frac{54}{36}}$

c)

$\sqrt{\frac{16}{400}}$

d)

$\sqrt{\frac{1}{20}}$

18.

Which one is a perfect square number?

a)

$\sqrt{\frac{1}{4}}$

b)

$\sqrt{\frac{2}{25}}$

c)

$\sqrt{\frac{4}{10}}$

d)

$\sqrt{\frac{50}{100}}$

19.

Which one is a perfect square number?

a)

$\sqrt{\frac{1}{3}}$

b)

$\sqrt{\frac{15}{45}}$

c)

$\sqrt{\frac{81}{111}}$

d)

$\sqrt{\frac{25}{49}}$

20.

Which one is NOT a perfect square number?

a)

$\sqrt{\frac{1}{9}}$

b)

$\sqrt{\frac{1}{2}}$

c)

$\sqrt{\frac{81}{121}}$

d)

$\sqrt{\frac{49}{361}}$

21.

Which is NOT a perfect square number?

a)

$\sqrt{0.4}$

b)

$\sqrt{0.04}$

c)

$\sqrt{4.41}$

d)

$\sqrt{0.64}$

22.

Which one is a perfect square number?

a)

$\sqrt{14.4}$

b)

$\sqrt{6.4}$

c)

$\sqrt{0.324}$

d)

$\sqrt{3.24}$

23.

Which one is NOT a perfect square number?

a)

$\sqrt{\frac{4000}{9000}}$

b)

$\sqrt{\frac{10000}{64000000}}$

c)

$\sqrt{\frac{490000}{1210000}}$

d)

$\sqrt{\frac{900}{2500}}$

24.

What is

\sqrt{\frac{5}{20}}

a)

$\frac{25}{400}$

b)

$\frac{1}{2}$

c)

$\frac{4}{5}$

d)

is not a perfect square

25.

Determine the value of $\sqrt[]{0.36}$

a)

0.06

b)

0.6

c)

0.7

d)

0.07

26.

What is the value of $\sqrt[]{0.49}$ ?

a)

0.5

b)

0.05

c)

0.7

d)

0.07

27.

What is the value of $\sqrt[]{0.81}$ ?

a)

0.9

b)

0.09

c)

0.55

d)

0.055

28.

What is the value of $\sqrt[]{\frac{1}{36}}$

a)

$\frac{1}{3}$

b)

$\frac{2}{3}$

c)

$\frac{1}{6}$

d)

$\frac{2}{6}$

29.

What is the value of $\sqrt[]{0.0225}$

a)

0.15

b)

0.015

c)

0.23

d)

0.023

30.

calculate the number whos square root is 0.12

a)

0.0144

b)

0.144

c)

0.48

d)

0.048

31.

Calculate the number whos square root is $\frac{2}{5}$

a)

$\frac{4}{25}$

b)

$\frac{2}{25}$

c)

$\frac{4}{5}$

d)

$\frac{2}{10}$

32.

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

33.

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

34.

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

35.

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

36.

Level 3: Which point best represents √47?

a)

A

b)

D

c)

E

d)

F

37.

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

38.

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

39.

Between which two whole numbers is the
√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

40.

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

a)

4.2

b)

4.4

c)

5.1

d)

4

41.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 23

a)

25

b)

16

c)

36

42.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 129

a)

121

b)

144

c)

100

43.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 91

a)

81

b)

100

c)

121

44.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 385

a)

361

b)

400

c)

441

45.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 186

a)

169

b)

196

c)

225

d)

182

46.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 228

a)

225

b)

256

c)

196

d)

232

47.

Estimate the following roots and select the best answer: √18

a)

4

b)

4.2

c)

4.9

d)

5.2

48.

Estimate the following roots and select the best answer: $\sqrt[]{66}$

a)

8.6

b)

9.3

c)

8.1

d)

7.5

49.

Estimate the following roots and select the best answer: √58

a)

7.1

b)

7.7

c)

7.06

d)

8.2

50.

The pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

51.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

52.

_{^{Find the missing side}}

a)

37

b)

17.66

c)

6

d)

312

53.

What is the length of x?

a)

5

b)

7

c)

8

d)

25

54.

a² + b² = c^{2
a = 9 b = 40}

a)

c = 41

b)

c = 65

c)

c = 25

d)

c = 5

55.

a² + b² = c^{2
b = 35 c = 37}

a)

a = 12

b)

a = 11

c)

a = 18

d)

a = 14

56.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

57.

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

a)

6

b)

6.7

c)

3

d)

15.7

e)

None of them

58.

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

59.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

60.

Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. What is the length of the diagonal, in yards, that Tanya runs?

a)

26.5 yards

b)

10 yards

c)

50 yards

d)

46.7 yards

61.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

MIDTERM - Squares, Roots & Pythagorean Theorem

Total questions: 61

Worksheet time: 6hrs 59mins

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