Free Printable Rationalization and Square Root Practice

1.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

2.

i⁷

a)

i

b)

-i

c)

1

d)

-1

3.

Calculate(Divide, multiply by conjugate):

a)

12/5 − 4/5i

b)

-8/10i − 4/5

c)

-4/5 + 12/5i

d)

12/5 + 4/5i

4.

Find the conjugate of:
-4 − 8i

a)

-4 + 8i

b)

4 − 8i

c)

4 + 8i

5.

Calculate (multiply):
(1 − 2i)(6 + 5i)

a)

16 − 7i

b)

-16 + 7i

c)

-16 − 7i

d)

16 + 7i

6.

Calculate (multiply):
(4 + 3i)(4 − 3i)

a)

16 − 9i²

b)

25

c)

7

d)

8 − 6i

7.

6i (-5 + 10i)

a)

-30i + 60i²

b)

30i − 16i²

c)

11i + 60i²

d)

-11i²+ 16i

8.

Calculate:
-4 (13 + 5i)

a)

-52 − 20i

b)

9 + i

c)

17 − 20i

d)

-52 + 20i

9.

Calculate:
(1 − 2i) + (-4 + 2i)

a)

-3

b)

-3 − 4i

c)

5 − 4i

d)

5

10.

Calculate:
(4 − 7i) − (-3 + 6i)

a)

7 − 13i

b)

7 − i

c)

1 − 13i

d)

1 − i

11.

Calculate:
i + 6i

a)

6i²

b)

7i

c)

5i

d)

7i²

12.

Simplify -√-8

a)

-i√8

b)

-2i√2

c)

2i√2

d)

-8i

13.

a)

(16 + 9i) / 13

b)

(16 + 9i) / 5

c)

(20 + 9i) / 13

d)

(20 + 9i) / 5

14.

a)

(9 + 15i) / 17

b)

(9 - 15i) / -8

c)

(9 - 15i) / (-8 - 15i)

d)

(9i + 15) / 17

15.

Simplify the expression:

a)

1

b)

9 - 4√4

c)

6 + 2√2

d)

1 - 4√2

16.

Simplify the following expression:

a)

b)

c)

d)

17.

a)

A

b)

B

c)

C

d)

D

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

Rationalize and Simplify. Leave answers in Standard Form.

a)

b)

c)

d)

25.

Simplify.

a)

b)

c)

d)

26.

Divide and simplify.

a)

4x√x

b)

3x²/x³√36

c)

2x

d)

4x²

27.

Rationalize the denominator.

a)

2x³

b)

(x√35x) / 5

c)

(x√7x) / 25

d)

49x⁷y / 5

28.

A number can be real AND imaginary.

a)

True

b)

False

29.

Simplify using the lowest power of i:

(-3i)(4i)(-5i)

a)

-60i

b)

60

c)

-60

d)

60i³

30.

Rationalize the expression.

Write the answer in standard form.

a)

b)

c)

d)

31.

Multiple Select:

Which numbers are complex numbers? Select ALL that apply!

a)

4i

b)

-3+2i

c)

1-4i

d)

3

32.

Rationalize the expression.

Write the answer in standard form.

a)

b)

c)

d)

33.

$\left(2x-3i\right)-\left(4x+6i\right)$

a)

$6x+3i$

b)

$8x^2-18i^2$

c)

$8x^2+18$

d)

$-2x-9i$

34.

Which answer choices are equivalent to $i^{17}$ ? Select all that apply!

a)

$i$

b)

$i^5$

c)

$i^{41}$

d)

$-1$

e)

$i^{-3}$

35.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

36.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

37.

Solve using the quadratic formula. What is the number under the radical, and what is the denominator? REMEMBER TO SIMPLIFY COMPLETELY!
$7x^2-2x+10$

a)

-276, 14

b)

-69, 14

c)

-69, 7

d)

-276, 7

e)

69, 7

38.

Solve using the quadratic formula. What is the number under the radical, and what is the denominator? REMEMBER TO SIMPLIFY COMPLETELY!
$3x^2+3x-7$

a)

-3, 6

b)

3, 6

c)

-3, 2

d)

3, 2

Rationalization and Square Root Practice

Total questions: 38

Worksheet time: 2hrs 37mins

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