Free Printable Roots and Radicals

1.

Write each expression in exponential form.

a)

A

b)

B

c)

C

d)

D

2.

Write each expression in exponential form.

a)

A

b)

B

c)

C

d)

D

3.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

4.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

5.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

6.

Evaluate without a calculator.

a)

A

b)

B

c)

C

d)

D

7.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

8.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

A

b)

B

c)

C

d)

D

11.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

14.

√5 × √10

a)

50

b)

2√5

c)

5√2

d)

5√10

15.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

16.

a)

-5√1

b)

8√2 + 13√3

c)

21√5

d)

20√5

17.

Simplify completely.

a)

3v√2v

b)

3v√2v³

c)

v√18v

d)

9v√v

18.

Simplify.

a)

5x⁸y¹⁰√10x

b)

5x⁴y⁵√10x

c)

5x⁴y⁵√2x

d)

5√2x⁹y¹⁰

19.

Simplify 9∛32

a)

9∛4

b)

2∛4

c)

18∛4

d)

9∛2

20.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

21.

Simplify this radical expression:

a)

b)

c)

d)

22.

a)

b)

c)

d)

23.

SIMPLIFY:

a)

A

b)

B

c)

C

d)

D

24.

Simplify.
∜-81

a)

-9

b)

9

c)

3

d)

not possible

25.

Simplify the expression:

a)

6x²y² ∛3

b)

6xy² ∛6x²

c)

∛1296x⁵y⁶

d)

cannot combine; unlike radicand

26.

Simplify

a)

3x²y²z√3yz

b)

3xyz√xy²

c)

3xyz

d)

Can't Simplify

27.

Simplify the above radical.

a)

b)

c)

d)

28.

Simplify the above radical.

a)

b)

c)

d)

29.

Simplify the above radical.

a)

b)

c)

d)

30.

Which of the following is correct?

a)

Root over Power

b)

Power over Root

31.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

32.

8

a)

W

b)

O

c)

R

d)

K

33.

2

a)

C

b)

A

c)

V

d)

E

34.

13

a)

True

b)

False

35.

Simplify the expression:
3^1/2 * 27^1/2

a)

9

b)

81

c)

3

d)

1/3

36.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

37.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

$4v^{\frac{1}{3}}$

b)

$\frac{4}{v^{\frac{1}{3}}}$

c)

$\frac{v^{\frac{1}{3}}}{4}$

d)

$\frac{1}{4v^{\frac{1}{3}}}$

38.

Simplify . Your answer should contain only positive exponents. $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

$\frac{x^{\frac{5}{3}}}{y^2}$

c)

$x^{\frac{5}{3}}y^2$

d)

$\frac{y^2}{x^{\frac{5}{3}}}$

39.

Simplify . Your answer should contain only positive exponents. $\frac{a^2b^0}{3a^4}$

a)

$1$

b)

$\frac{1}{3a^2}$

c)

$\frac{a^2}{3a^4}$

d)

$\frac{1}{3a^4}$

40.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

41.

Simplify . Your answer should contain only positive exponents. $u^{-\frac{5}{4}}v^2•\left(u^{\frac{3}{2}}\right)^{-\frac{3}{2}}$

a)

$\frac{v^2}{u^{\frac{7}{2}}}$

b)

$\frac{v^2}{u^{\frac{5}{2}}}$

c)

$\frac{v^2}{u^{\frac{5}{4}}}$

d)

$v^2$

42.

Simplify . Your answer should contain only positive exponents. $\frac{3y^{-\frac{5}{4}}}{y^{-1}•2y^{-\frac{1}{3}}}$

a)

$\frac{3y^{\frac{1}{12}}}{2}$

b)

$\frac{3y^{\frac{19}{12}}}{2}$

c)

$\frac{3}{2y^{\frac{1}{12}}}$

d)

$\frac{3}{2y^{\frac{19}{12}}}$

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

Rationalize the denominator.

a)

x/2

b)

∛(4x) / 2

c)

∛(2x) / 2

d)

2x

46.

a)

4

b)

-4

c)

2

d)

-2

47.

a)

2

b)

-2

c)

4

d)

-4

48.

a)

9

b)

-9

c)

21

d)

-21

49.

a)

3

b)

-3

c)

2

d)

0

50.

a)

7

b)

5

c)

-7

d)

-5

51.

a)

1

b)

-1

c)

0

d)

-2

52.

Solve the equation.

a)

n = 27

b)

n = 18

c)

n = -18

d)

n = 36

53.

a)

x=19

b)

x= -30

c)

x= -9

d)

No Solution

54.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

55.

Solve. (3x-5)^1/4+3=4

a)

4/3

b)

2

c)

-2

d)

-4/3

56.

Solve. (2x-5)^1/3=3

a)

16

b)

3

c)

7

d)

no solution

57.

Solve. (2x-8)^2/3= 4

a)

x = 8, x= 0

b)

x = 8

c)

x = 7, x = -2

d)

no solution

58.

Solve. (6x-3)^2/3 + 6 = 15

a)

x = -5, x = 4

b)

x = 5

c)

x = 5, x = -4

d)

no solution

59.

Rewrite the expression without using a radical:

a)

(2x+1)^3/4

b)

(2x+1)^4/3

c)

4(2x+1)³

d)

3(2x+1)⁴

60.

Solve for x:

a)

6

b)

7

c)

8

d)

9

61.

Solve for x:
(2x - 1)^3/4 + 9 = 36

a)

27

b)

13

c)

41

d)

82

62.

Solve for m

a)

m=2

b)

m=18

c)

m=2 and m=18

d)

m=-2 and m=-18

63.

Solve for p

a)

p=-7 and p=62/9

b)

p=7 and p=-62/9

c)

p=7

d)

p=-7

Roots and Radicals

Total questions: 63

Worksheet time: 5hrs 15mins

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