Free Printable A2-CHAPTER 5 TEST 2025-26

1.

Find the indicated real n^th root(s) of a.

n = 6, a = −729

a)

3

b)

-3

c)

±3

d)

no real roots

2.

Find the indicated real n^th root(s) of a.

n = 5 , a = -243

a)

3

b)

-3

c)

±3

d)

no real roots

3.

Find the indicated real n^th root(s) of a.

n = 4, a = 256

a)

-4

b)

4

c)

±4

d)

no real roots

4.

Find the indicated real n^th root(s) of a.

n = 3, a = 8

a)

±2

b)

2

c)

-2

d)

no real roots

5.

Find the indicated nth root(s) of a.

n =3, a = -125

a)

5

b)

-5

c)

41.6666

d)

$\pm5$

6.

n = 2, a = 400

a)

20

b)

-20

c)

$\pm20$

d)

200

7.

n = 6, a = 64

a)

2

b)

-2

c)

10

d)

$\pm2$

8.

Find the indicated nth root(s) of a

n=3, a=8

(a)

9.

Find the indicated nth root(s) of a

n=5, a=-32

(a)

10.

Find the nth roots of a:
n=4; a=256

a)

8

b)

±8

c)

4

d)

±4

11.

Simplify

^3\sqrt{125}

a)

5

b)

15

c)

25

d)

41.7

12.

Simplify

^5\sqrt{-32}

a)

2

b)

-2

c)

6.4

d)

-6.4

13.

Fill in the blank: Every positive real number has ___ real nth roots when n is odd.

a)

2

b)

1

c)

0

d)

$\infty$

14.

Fill in the blank: Every negative real number has ___ real nth roots when n is even.

a)

2

b)

1

c)

0

d)

$\infty$

15.

Fill in the blank: Every negative real number has ___ real nth roots when n is odd.

a)

2

b)

1

c)

0

d)

$\infty$

16.

Find the cube root(s): ∛1

a)

1

b)

-1

c)

±1

d)

none

17.

$^3\sqrt{-64}=$

a)

-8

b)

8

c)

-4

d)

4

18.

a)

11

b)

576

c)

-12

d)

-13

19.

√-169

a)

-13

b)

13

c)

14

d)

-14

e)

Does not exist

20.

What is the root index for the square root of 9?

a)

1

b)

2

c)

3

d)

4

21.

Simplify the following

a)

4

b)

9

c)

2

d)

3

22.

Find the indicated nth root.

a)

-7

b)

7

c)

No Real Solutions

d)

5

23.

Find the indicated nth root.

a)

6

b)

-6

c)

No Real Solutions

d)

Infinite Solutions

24.

Find the indicated nth root.

a)

No Real Solutions

b)

-2

c)

2

d)

Infinite Solutions

25.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

26.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

27.

Find the cube root.

SIMPLIEST FORM

a)

9/12

b)

3/4

c)

4/8

d)

5/4

e)

2/6

28.

$\sqrt{\frac{81}{225}}$ Find the square root

a)

3/5

b)

5/3

c)

3/4

d)

4/3

29.

CHO0SE BEST ANSWER

a)

3/2

b)

2/3

c)

4/9

d)

-4/9

30.

Evaluate.

a)

7/5

b)

±7/5

c)

5/7

d)

±5/7

31.

CHOOSE BEST ANSWER

a)

27/8

b)

-27/8

c)

3/2

d)

2/3

32.

CHOOSE BEST ANSWER

a)

1

b)

2

c)

0

33.

a)

0

b)

1

c)

2

34.

a)

0

b)

1

c)

2

35.

CHOOSE BEST ANSWER

a)

3/10,-3/10

b)

-3/10,-3/10

c)

3/10

d)

-3/10

36.

CHOOSE BEST ANSWER

a)

3/4,-3,4

b)

-3/4,-3/4

c)

-3/4

d)

3/4

37.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

38.

Simplify
√98b

a)

√98

b)

9√9b

c)

7√2b

d)

7√8b

39.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

40.

a)

A

b)

B

c)

C

d)

D

41.

a)

A

b)

B

c)

C

d)

D

42.

a)

A

b)

B

c)

C

d)

D

43.

√343k⁴

a)

7k²√7

b)

49k²√7

c)

6k²√7

d)

k²√7

44.

5√48x²

a)

10x√3

b)

15x√3

c)

20x√3

d)

25x√3

45.

√36x³y⁴

a)

6y²x√x

b)

3y²√2x

c)

3y√x

d)

6x√3y

46.

√28m⁴n³

a)

m²n√7n

b)

7m²n√n

c)

2m²n√7n

d)

7m²n²√n

47.

-3√20x⁴y²

a)

-6x²y√5

b)

6xy√5

c)

-3xy√2

d)

3x²y√5

48.

√96p⁹

a)

4p³

b)

4p⁴√p

c)

4p⁴√6p

d)

4p⁴√2p

49.

5√48x²

a)

10x√3

b)

15x√3

c)

20x√3

d)

25x√3

50.

Simplify the expression

a)

6a⁵b³√6b

b)

2a⁵b³√54b

c)

3a⁵b³

d)

6√2a¹⁰b⁷

51.

The expression $\sqrt{x^{33}}$ is equivalent to

a)

$x^{16}\sqrt{x}$

b)

$x^4\sqrt{x}$

c)

$x^8\sqrt{x}$

d)

$x^2\sqrt{x}$

52.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

53.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

54.

√36x³y⁴

a)

6y²x√x

b)

3y²√2x

c)

3y√x

d)

6x√3y

55.

√28m⁴n³

a)

m²n√7n

b)

7m²n√n

c)

2m²n√7n

d)

7m²n²√n

56.

√75x²

a)

5x²√3

b)

5x

c)

5x√3x

d)

5x√3

57.

$12\sqrt{48x^5y^7z}$

a)

$48x^2y^3\sqrt{3xz}$

b)

$16x^2y^3\sqrt{3xz}$

c)

$72x^2y^2\sqrt{8x^2y^4z}$

d)

None of the above

58.

$\sqrt{192k^7q^8}$

a)

$8q^4\sqrt{3k^7}$

b)

$8k^3q^4\sqrt{3}$

c)

$8k^3q^4\sqrt{3k}$

d)

$8k^7q^8\sqrt{3k}$

59.

Simplify the expression

a)

6a⁵b³√6b

b)

2a⁵b³√54b

c)

3a⁵b³

d)

6√2a¹⁰b⁷

60.

$Simplify.$

a)

b)

c)

d)

61.

$Simplify.$

a)

b)

c)

d)

62.

$Simplify.$

a)

b)

c)

d)

63.

$Simplify.$

a)

b)

c)

d)

64.

$Simplify.$

a)

b)

c)

d)

65.

$Simplify.$

a)

b)

c)

d)

66.

$Simplify.$

a)

b)

c)

d)

67.

$Simplify>$

a)

b)

c)

d)

68.

$Simplify.$

a)

b)

c)

d)

69.

$Simplify.$

a)

b)

c)

d)

70.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

71.

a)

x⁴y⁴√y

b)

72xy

c)

xy√y

d)

x²y³√x²

72.

a)

A

b)

B

c)

C

d)

D

73.

a)

A

b)

B

c)

C

d)

D

74.

a)

A

b)

B

c)

C

d)

D

75.

What is the square root of -1?

a)

-1

b)

i

c)

1

d)

0

76.

What is the cube root of -8?

a)

-4

b)

0

c)

2

d)

-2

77.

What is the fourth root of 16?

a)

2

b)

8

c)

4

d)

10

78.

What is the fifth root of -32?

a)

-1

b)

2

c)

0

d)

-2

79.

What is the sixth root of 64?

a)

4

b)

8

c)

16

d)

2

80.

What is the cube root of -27?

a)

0

b)

-3

c)

-9

d)

3

81.

What is the fifth root of 243?

a)

3

b)

2

c)

5

d)

4

82.

Estimate √5 to the nearest three decimal places

a)

2.236

b)

2.500

c)

4.472

d)

25

83.

Solve each equation for x:

a)

9

b)

3

c)

6

d)

12

84.

√ 64

a)

4

b)

6

c)

9

d)

8

85.

Solve ∛729

a)

6

b)

7

c)

8

d)

9

86.

Estimate the square root.

a)

4.876

b)

5.385

c)

10.77

d)

14.5

87.

Solve m³= 343

a)

6

b)

16

c)

7

d)

17

88.

a)

.6

b)

6

c)

0.06

d)

Answer Not Here

89.

What is the most accurate value of the 5th root of 100.

a)

50.000

b)

20.000

c)

15.346

d)

2.512

90.

$x^3=\ 100$

What is the most accurate solution for x?

a)

33.333

b)

30

c)

4.642

d)

5.344

91.

Simplify

a)

√5

b)

-3√6

c)

√6

d)

6

92.

a)

6m²

b)

36

c)

6

d)

93.

a)

b)

c)

d)

94.

Simplify:
√10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

95.

√3 × √15 =

a)

3√5

b)

5√3

c)

2√7

d)

√17

96.

Find the area of the rectangle shown.

a)

18√20

b)

12√10 + 6√2

c)

9√12

d)

36√5

97.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

98.

Simplify

a)

b)

c)

d)

e)

99.

Simplify

a)

40

b)

√14

c)

-10√10

d)

2√10

100.

Simplify:
√10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

101.

Simplify

a)

b)

c)

d)

e)

102.

a)

A

b)

B

c)

C

d)

D

103.

$\sqrt{10x^2}\cdot\ \sqrt{10x}$

a)

$10x\sqrt{x}$

b)

$100\sqrt{x^3\ }$

c)

$10x^2\sqrt{x}$

d)

$x\sqrt{100x}$

104.

$-4\sqrt{15}\cdot2\sqrt{5}$

a)

$-8\sqrt{75}$

b)

$-30\sqrt{15}$

c)

$-40\sqrt{3}$

d)

$-600$

105.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

106.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

107.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

108.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

109.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

110.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

111.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

112.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

113.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

114.

Write your answer in simplest form

a)

A

b)

B

c)

C

d)

D

115.

Multiply the radicals using the distributive property:

$\sqrt[]{6}\left(\sqrt[]{3}+\sqrt[]{10}\right)$

a)

$2\sqrt[]{3}+4\sqrt[]{15}$

b)

$3\sqrt[]{2}+2\sqrt[]{15}$

c)

$3\sqrt[]{15}+3\sqrt[]{2}$

d)

$18\sqrt[]{10}$

116.

Multiply the radicals using the distributive property:

$-5\sqrt[]{5}\left(5+\sqrt[]{3}\right)$

a)

$-25\sqrt[]{3}$

b)

$-5\sqrt[]{15}$

c)

$-25\sqrt[]{5}-5\sqrt[]{15}$

d)

$-25\sqrt[]{15}-5\sqrt[]{5}$

117.

Multiply the radicals using the distributive property:

$3\sqrt[]{3}\left(-4\sqrt[]{10}+5\sqrt[]{3}\right)$

a)

$-12\sqrt[]{30}+45$

b)

$-12\sqrt[]{3}+45$

c)

$-12\sqrt[]{3}+15$

d)

$-3\sqrt[]{15}+30$

118.

Multiply the radicals using the distributive property:

$\left(2\sqrt[]{3}-2\right)\left(\sqrt[]{3}-1\right)$

a)

$6-\sqrt[]{3}$

b)

$8-4\sqrt[]{3}$

c)

$3-\sqrt[]{6}$

d)

$8-4\sqrt[]{6}$

119.

Multiply the radicals using the distributive property:

$\left(\sqrt[]{3}+\sqrt[]{2}\right)\left(\sqrt[]{3}-\sqrt[]{2}\right)$

a)

$-3\sqrt[]{6}$

b)

$-2\sqrt[]{6}$

c)

$-6$

d)

$1$

120.

Multiply the radicals using the distributive property:

$\left(5\sqrt[]{5}+4\sqrt[]{2}\right)\left(-2\sqrt[]{5}+2\sqrt[]{2}\right)$

a)

$34+2\sqrt[]{10}$

b)

$-17+2\sqrt[]{10}$

c)

$-34+2\sqrt[]{10}$

d)

$17+2\sqrt[]{10}$

121.

Multiply the radicals using the distributive property:

$\left(4-3\sqrt[]{2}\right)\left(4+3\sqrt[]{2}\right)$

a)

$-2$

b)

$8$

c)

$-8$

d)

$16$

122.

Multiply the radicals using the distributive property:

$\left(1-4\sqrt[]{2}\right)\left(4+\sqrt[]{2}\right)$

a)

$-4+2\sqrt[]{8}$

b)

$-4-15\sqrt[]{2}$

c)

$4-2\sqrt[]{8}$

d)

$-4-2\sqrt[]{8}$

123.

CHOOSE BEST ANSWER

a)

A

b)

B

c)

C

d)

D

124.

CHOOSE BEST ANSWER

a)

A

b)

B

c)

C

d)

D

125.

Multiply the radicals:

$\sqrt[]{7}\cdot\sqrt[]{14}$

a)

$7\sqrt[]{2}$

b)

$7$

c)

$\sqrt[]{14}$

d)

$14$

126.

Multiply the radicals using the distributive property:

$\left(\sqrt[]{5}+\sqrt[]{4}\right)\left(\sqrt[]{5}-\sqrt[]{4}\right)$

a)

$-5\sqrt[]{4}$

b)

$-4\sqrt[]{5}$

c)

$-5$

d)

$1$

127.

Multiply the radicals:

$3\sqrt[]{10}\cdot2\sqrt[]{5}$

a)

$30\sqrt[]{2}$

b)

$30$

c)

$60$

d)

$60\sqrt[]{2}$

128.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

$-\frac{\left(3-3\sqrt{5}\right)}{2}$

129.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

130.

Rationalize the following: $\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$

a)

$\frac{\sqrt{6}-\sqrt{10}}{8}$

b)

$\frac{\sqrt{6}-\sqrt{10}}{-2}$

c)

$\frac{\sqrt{6}+\sqrt{10}}{8}$

d)

$\frac{2\sqrt{3}+2\sqrt{5}}{-2}$

131.

$\frac{-2}{1+\sqrt{6}}$ Rationalize the following:

a)

$\frac{1+\sqrt{6}}{-2}$

b)

$\frac{-2+2\sqrt{6}}{-5}$

c)

$-\frac{2\sqrt{6}}{6}$

d)

$-2\sqrt{6}$

132.

Rationalize the denominator: $\frac{18}{-4-\sqrt{3}}$

a)

$\frac{54\sqrt{3}}{-19}$

b)

$\frac{-54\sqrt{3}}{13}$

c)

$\frac{-72+18\sqrt{3}}{13}$

d)

$\frac{-72+18\sqrt{3}}{19}$

133.

Rationalize the Denominator:
$\frac{4}{3-\sqrt{2}}$

a)

$\frac{12+4\sqrt{2}}{7}$

b)

$\frac{3+\sqrt{2}}{4}$

c)

$\frac{12-2\sqrt{2}}{3}$

d)

$\frac{4-12\sqrt{2}}{7}$

134.

Rationalize the Denominator:

\frac{3}{3-\sqrt{3}}

a)

$\frac{3+\sqrt{3}}{3}$

b)

$2+\sqrt{2}$

c)

$\frac{3+\sqrt{3}}{2}$

d)

$3+\sqrt{3}$

135.

Rationalize the Denominator:

$\frac{\sqrt{3}}{2+4\sqrt{3}}$

a)

$\frac{\sqrt{3}+6}{22}$

b)

$22+\sqrt{3}$

c)

$6+\sqrt{22}$

d)

$\frac{-\sqrt{3}+6}{22}$

136.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

$-\frac{\left(3-3\sqrt{5}\right)}{2}$

137.

Rationalize the Denominator:
$\frac{5}{2+\sqrt{3}}$

a)

$\frac{10-5\sqrt{3}}{1}$

b)

$\frac{10-5\sqrt{3}}{4-3}$

c)

$\frac{10+5\sqrt{3}}{1}$

d)

$\frac{10-5\sqrt{3}}{1}$

138.

Rationalize the Denominator:

$\frac{7}{1+\sqrt{2}}$

a)

$-1-\sqrt{2}$

b)

$1-\sqrt{2}$

c)

$1+\sqrt{2}$

d)

$\sqrt{2}$

139.

Rationalize the Denominator:
$\frac{2\sqrt{5}}{3-\sqrt{5}}$

a)

$\frac{6\sqrt{5}+10}{4}$

b)

$\frac{6\sqrt{5}-10}{4}$

c)

$\frac{2\sqrt{5}-3}{4}$

d)

$\frac{2\sqrt{5}+3}{4}$

A2-CHAPTER 5 TEST 2025-26

Total questions: 139

Worksheet time: 5hrs 11mins

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