Free Printable U6

1.

Write the expression in simplest radical form.

$\sqrt[]{245x^{10}}$

2.

Write the expression in simplest radical form.

$\sqrt[]{600x^9y^{16}}$

3.

Write the expression in simplest radical form.

$\sqrt{45}$

4.

Write the expression in simplest radical form.

$\sqrt{54}$

5.

Write the expression in simplest radical form.

$7\sqrt{144x^4}$

6.

Write the expression in simplest radical form.

$7\sqrt{24x}$

7.

Write the expression in simplest radical form.

$\sqrt{245x^3y^4}$

8.

Write the expression in simplest radical form.

$\sqrt{54xy^4}$

9.

Write the expression in simplest radical form.

10.

Write the expression in simplest radical form.

$\sqrt[]{98}$

11.

Write the expression in simplest radical form.

$\sqrt[]{28}\ \sqrt[]{3}$

12.

Write in simplest radical form:

13.

Write in simplest radical form

14.

Write the expression in simplest radical form

$\sqrt[]{300}$

15.

Write the expression in simplest radical form.

$\sqrt[]{150}$

16.

Write the expression in simplest radical form.

$3\ \sqrt[]{700}$

17.

Write the expression in simplest radical form.

$2\ \sqrt[]{24}$

18.

Write the expression in simplest radical form.

$2\ \sqrt[]{50}$

19.

Write the expression in simplest radical form

$\sqrt[]{10x^5}\ \sqrt[]{5xy}$

20.

Write the expression in simplest radical form

$\sqrt[]{6xy}\ \sqrt[]{2x^3y^3}$

21.

Write the expression in simplest radical form.

$2\ \sqrt[]{8x^3}⋅9\ \sqrt[]{18x}$

22.

_{^{Find the missing side. Write your answer in simplest radical form.}}

23.

Find the missing side. Write your answer in simplest radical form.

24.

Find the value of c. Write your answer in simplest radical form.

25.

Solve for y. Write your answer in simplest radical form.

26.

Solve for y. Write your answer in simplest radical form.

27.

Solve for x. Write your answer in simplest radical form.

28.

Solve for x. Write your answer in simplest radical form.

29.

Solve for the missing side. Write your answer in simplest radical form.

30.

Solve for the missing side. Write your answer in simplest radical form.

31.

Solve for the missing side. Write your answer in simplest radical form.

32.

Solve for the missing side. Write your answer in simplest radical form.

33.

Solve for the missing side. Write your answer in simplest radical form.

34.

Solve for the missing side. Write your answer in simplest radical form.

35.

Solve for the missing side. Write your answer in simplest radical form.

36.

Solve for the missing side. Write your answer in simplest radical form.

37.

Solve for the missing side. Write your answer in simplest radical form.

38.

Solve for the missing side. Write your answer in simplest radical form.

39.

Solve for the missing side. Write your answer in simplest radical form.

40.

Write in simplest radical form.

$\sqrt[]{28x^6}$

41.

Write in simplest radical form.

$4\sqrt[]{45x^7}$

42.

Write in simplest radical form.

$7\sqrt[]{20x^3}$

43.

Write in simplest radical form.

$\frac{\sqrt[]{5}}{3\sqrt[]{2}}$

44.

a)

A

b)

B

c)

C

d)

D

45.

Write in simplest radical form.

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

Write in simplest radical form.

50.

Write in simplest radical form.

$\frac{4}{\sqrt{5}}$

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

A

b)

B

c)

C

d)

D

53.

Write in simplest radical form.

54.

Write in simplest radical form.

$\frac{12}{\sqrt[]{2}}$

55.

Write in simplest radical form.

$\frac{7\sqrt[]{3}}{\sqrt[]{5}}$

56.

Write in simplest radical form.

$\frac{\sqrt[]{4}}{\sqrt[]{5}}$

57.

Write in simplest radical form.

$\frac{\sqrt[]{16}}{\sqrt[]{3}}$

58.

Write in simplest radical form.

$\frac{\sqrt[]{7}}{\sqrt[]{18}}$

59.

Write in simplest radical form.

$\frac{8}{\sqrt[]{20}}$

60.

Write in simplest radical form.

$\frac{3\sqrt[]{6}}{\sqrt[]{2}}$

61.

Write in simplest radical form.

$\frac{2\sqrt[]{5}}{\sqrt[]{75}}$

62.

Simplify. Write your answer in simplest radical form.

$3\sqrt[]{8}+3\sqrt[]{2}$

63.

Simplify. Write your answer in simplest radical form.

$-10\sqrt[]{7}+12\sqrt[]{7}$

64.

Simplify. Write your answer in simplest radical form.

65.

Simplify the expression. Write your answer in simplest radical form. $-2\sqrt{3}-2\sqrt{27}-\sqrt{27}$

66.

Simplify. Write your answer in simplest radical form.

$2\sqrt[]{3}+2\sqrt[]{8}-3\sqrt[]{3}$

67.

Simplify the expression. Write your answer in simplest radical form.

68.

Simplify. Write your answer in simplest radical form.

69.

Simplify the expression. Write your answer in simplest radical form.

$-\sqrt{54}-2\sqrt{24}$

70.

Simplify. Write your answer in simplest radical form.

$3\sqrt[]{8}+3\sqrt[]{2}$

71.

Simplify. Write your answer in simplest radical form.

$-3\sqrt[]{20}-\sqrt[]{5}$

72.

Simplify. Write your answer in simplest radical form.

$2\sqrt[]{45}-2\sqrt[]{5}$

73.

Simplify. Write your answer in simplest radical form.

$-3\sqrt[]{18}+3\sqrt[]{8}-\sqrt[]{24}$

74.

Simplify. Write your answer in simplest radical form.

$-3\sqrt[]{18}\cdot2\sqrt[]{24}$

75.

Simplify. Write your answer in simplest radical form.

$2\sqrt[]{45}\cdot2\sqrt[]{5}$

76.

Simplify. Write your answer in simplest radical form.

$3\sqrt[]{8}\cdot3\sqrt[]{2}$

77.

Simplify the expression. Write your answer in simplest radical form.

$2\sqrt[]{18}\cdot\sqrt[]{27}\cdot\sqrt[]{50}$

78.

Simplify the expression. Write your answer in simplest radical form.

$-2\sqrt[]{20}+2\sqrt[]{18}-2\sqrt[]{5}$

79.

Simplify the expression. Write your answer in simplest radical form.

$-2\sqrt[]{20}\cdot2\sqrt[]{18}\cdot2\sqrt[]{5}$

80.

Simplify the expression. Write your answer in simplest radical form.

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

81.

Simplify the expression. Write your answer in simplest radical form.

$-3\sqrt[]{3}\cdot\sqrt[]{8}\cdot3\sqrt[]{3}$

82.

Simplify. Write in simplest radical form.

$-2\sqrt[]{15}\left(-3\sqrt[]{3}+3\sqrt[]{5}\right)$

83.

Simplify. Write in simplest radical form.

$5\sqrt[]{42}\left(4+4\sqrt[]{7}\right)$

84.

Simplify. Write in simplest radical form.

$2\sqrt[]{14}\left(3-\sqrt[]{7}\right)$

85.

Simplify. Write in simplest radical form.

$\left(-2\sqrt[]{3}+6\right)\left(4-\sqrt[]{7}\right)$

86.

Simplify. Write in simplest radical form.

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

87.

Simplify. Write in simplest radical form.

$\left(6-2\sqrt[]{3}\right)\left(7+\sqrt[]{3}\right)$

88.

Simplify. Write in simplest radical form.

$\left(5-\sqrt[]{7}\right)\left(5+\sqrt[]{7}\right)$

89.

Simplify. Write in simplest radical form.

$-2\sqrt[]{15}\cdot3\sqrt[]{3}\cdot3\sqrt[]{5}$

90.

Simplify. Write in simplest radical form.

$6\left(2\sqrt[]{3}\right)\cdot7\sqrt[]{3}$

91.

Simplify. Write in simplest radical form.

$2\sqrt[]{3}+7\sqrt[]{3}+5\sqrt[]{18}$

92.

Simplify. Write in simplest radical form.

$6-2\sqrt[]{3}+7+\sqrt[]{3}$

93.

a)

A

b)

B

c)

C

d)

D

94.

a)

A

b)

B

c)

C

d)

D

95.

a)

A

b)

B

c)

C

d)

D

96.

Simplify. Write answers in simplest radical form.

$\frac{\sqrt[]{7}}{5-\sqrt[]{11}}$

97.

Simplify. Write answers in simplest radical form.

$\frac{\sqrt[]{8}}{2+\sqrt[]{3}}$

98.

Simplify. Write answers in simplest radical form.

$\frac{5}{\sqrt[]{7}+\sqrt[]{3}}$

99.

Simplify. Write answers in simplest radical form.

$\frac{\sqrt[]{6}}{5\sqrt[]{2}+7}$

100.

Simplify. Write answers in simplest radical form.

$5\sqrt[]{2}+7\sqrt[]{18}$

101.

Simplify. Write answer in simplest radical form.

$5\sqrt[]{18}+4\sqrt[]{32}$

102.

Simplify. Write your answer in simplest radical form.

$2\sqrt[]{3}\left(5\sqrt[]{12}-4\right)$

103.

Simplify. Write your answer in simplest radical form.

$\left(2\sqrt[]{3}+\sqrt[]{5}\right)\left(\sqrt[]{8}-4\right)$

104.

Simplify. Write your answer in simplest radical form.

$\frac{11\sqrt[]{3}}{7-2\sqrt[]{5}}$

105.

Simplify. Write answer in simplest radical form.

$5\sqrt[]{18}\cdot4\sqrt[]{36}$

106.

Simplify. Write answer in simplest radical form.

$\frac{5}{7\sqrt[]{3}}$

107.

Solve. Identify the solution.

$\sqrt{8x+8}-20=-12$

(a)

108.

Solve.

$\sqrt{2x-6}=x-3$

a)

Solution: x=3 and x=5

b)

Solution: x=3

Extraneous Solution: x=5

c)

Solution: x=5

Extraneous Solution: x=3

d)

No Solutions

Extraneous Solutions: x=3 and x=5

109.

Solve.

$\sqrt{14-5x}=x-4$

a)

Solutions: x=1 and x=2

b)

Solution: x=1

Extraneous Solution: x=2

c)

Solution: x=2

Extraneous Solution: x=1

d)

No Solution

Extraneous Solutions: x=1 and x=2

110.

Solve. Identify the solution.

(a)

111.

Solve. Identify the solution.

$x=\sqrt{8-7x}$

(a)

112.

Solve. Identify the extraneous solution.

$x=\sqrt{8-7x}$

(a)

113.

Solve.

$\sqrt[]{11-5x}=x-1$

a)

Solution: x=2

Extraneous Solution: x=-5

b)

Solution: x=-5

Extraneous Solution: x=2

c)

Solutions: x=2 and x=-5

d)

No Solutions

Extraneous Solutions: x=2 and x=-5

114.

Solve. Identify the solution

$\sqrt[]{x^2-3x+36}=x+3$

(a)

115.

Solve. Identify the solution.

$x=\sqrt[]{12-x}$

(a)

116.

Solve. Identify the extraneous solution.

$x=\sqrt[]{12-x}$

(a)

117.

Solve. Identify the solution.

$\sqrt[]{41-4x}=x-5$

(a)

118.

Solve. Identify the extraneous solution.

$\sqrt[]{41-4x}=x-5$

(a)

119.

Solve. Identify the solution.

$-x=\sqrt[]{18-7x}$

(a)

120.

Solve. Identify the extraneous solution.

$-x=\sqrt[]{18-7x}$

(a)

121.

Match the following

a)

1.

D:{x>=0}

R:{y>=0}

b)

2.

D:{x>=0}

R:{y<=0}

c)

3.

Not a function

d)

4.

D:{x<=0}

R:{y<=0}

e)

5.

D:{x<=0}

R:{y>=0}

122.

Match the following

a)

1.

Radical Function

R:{y>=2}

b)

2.

Quadratic Function

R:{y>=2}

c)

3.

Not a function

d)

4.

Quadratic Function

R:{y>=0}

e)

5.

Radical Function

R:{y>=0}

123.

Select all that apply

$y=\sqrt[]{x-3}-4$

a)

$D:\left\{x\ge3\right\}$

b)

$D:\left\{x\ge-3\right\}$

c)

$R:\left\{y\ge4\right\}$

d)

$R:\left\{y\ge-4\right\}$

e)

Starting point is (-3, -4)

124.

Select all that apply

$y=\sqrt[]{x+5}-2$

a)

$D:\left\{x\ge-5\right\}$

b)

$D:\left\{x\ge5\right\}$

c)

$R:\left\{y\ge2\right\}$

d)

$R:\left\{y\ge-2\right\}$

e)

Starting point is (-5, -2)

125.

Which equation is shown?

a)

$y=\sqrt[]{x-3}$

b)

$y=\sqrt[]{x+3}$

c)

$y=\sqrt[]{x}-3$

d)

$y=\sqrt[]{x}+3$

126.

Which equation is shown?

a)

$y=\sqrt[]{x-2}$

b)

$y=\sqrt[]{x+2}$

c)

$y=\sqrt[]{x}-2$

d)

$y=\sqrt[]{x}+2$

127.

What is the domain of the given graph? Use correct notation.

(a)

128.

What is the range of the given graph? Use correct notation.

(a)

129.

What is the domain of the given graph? Use correct notation.

(a)

130.

What is the range of the given graph? Use correct notation.

(a)

131.

Match the following

a)

$y=a\left|x-h\right|+k$

1.

Absolute Value Function

b)

$y=a\left(x-h\right)^2+k$

2.

Quadratic Function in Vertex Form

c)

$y=ax^2+bx+c$

3.

Quadratic Function in Standard Form

d)

$y=a\sqrt[]{x-h}+k$

4.

Radical Function

e)

$y=mx+b$

5.

Linear Function

132.

Match the following

a)

1.

Absolute Value Function

b)

2.

Quadratic Function

c)

3.

Exponential Function

d)

4.

Radical Function

e)

5.

Linear Function

133.

Which is the graph of the following equation?

$y=\sqrt[]{x+4}$

a)

b)

c)

d)

134.

Which is the graph of the following equation?

$y=\sqrt[]{x+2}-2$

a)

b)

c)

d)

U6 - Radicals

Total questions: 134

Worksheet time: 3hrs 2mins

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