Free Printable Simplifying Radical Expressions Review

1.

Which is equivalent to √121p⁵r⁷s⁴?

a)

11prs √pr

b)

11p^2.5r^3.5s²√pr

c)

11p²r³s²√pr

d)

11p²r³s²

2.

Simplfiy

a)

5√2

b)

0

c)

2√2

d)

-3√2

3.

Simplify

a)

√5

b)

-3√6

c)

√6

d)

6

4.

Simplify

a)

9

b)

5√2 + 2

c)

10√2

d)

2√2 + 3√30

5.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

6.

a)

3√3x

b)

3√x

c)

2√3x

d)

2√x

7.

The square root of 36x² is __________

a)

6

b)

6x

c)

4x

d)

6x²

8.

The square root of 64x⁸y⁶is ?

a)

32x⁴y³

b)

8xy

c)

8x⁴y³

d)

16

9.

The square root of 25x⁶is ?

a)

25x

b)

5x²

c)

5x³

d)

x³

10.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

11.

Simplify the radical expression:
$\sqrt{2x^2y^3}$

a)

$2y\sqrt{xy}$

b)

$2x\sqrt{y^2}$

c)

$y\sqrt{2xy}$

d)

$xy\sqrt{2y}$

12.

Simplify the radical:
$\sqrt{98}$

a)

$2\sqrt{7}$

b)

$7\sqrt{2}$

c)

$14\sqrt{2}$

d)

$49\sqrt{2}$

13.

Simplify the radical:
$\sqrt{180}$

a)

$5\sqrt{6}$

b)

$5\sqrt{5}$

c)

$13\sqrt{5}$

d)

$6\sqrt{5}$

14.

Simplify the radical expression:
$\sqrt[3]{96r^8s^3}$

a)

$2r^2s\sqrt[3]{12r^2}$

b)

$2r^4s\sqrt[3]{6}$

c)

$r^2s\sqrt[3]{96r}$

d)

$4r^4s\sqrt[3]{6s}$

15.

Simplify the radical expression:
$\sqrt{63x^2y^5}$

a)

$3xy^2\sqrt{7y}$

b)

$9xy\sqrt{7y}$

c)

$3y\sqrt{7xy^2}$

d)

$7y^2\sqrt{9xy}$

16.

Simplify the radical expression:
$2\sqrt{56a^2b^2}$

a)

$4ab\sqrt{14}$

b)

$2ab\sqrt{14}$

c)

$14ab\sqrt{2ab}$

d)

$14\sqrt{2ab}$

17.

Solve: 4∛5 + 6∛5 − 9∛5

a)

19∛5

b)

10∛5 - 9∛5

c)

-∛5

d)

∛5

18.

Solve: 3√6 + 3√2 - 5√6 - 2√2

a)

-2√6 + √2

b)

-√2

c)

6√2 - 7√6

d)

2√6 - √2

19.

√18 - √12

a)

√6

b)

2√3

c)

√2

d)

√5

20.

a)

13√3

b)

10√30

c)

13√6

d)

11√3

21.

6√50 + √2

a)

12√2

b)

31√2

c)

18√2

d)

12√5

22.

√5 × √10

a)

50

b)

2√5

c)

5√2

d)

5√10

23.

√3 × √15 =

a)

3√5

b)

5√3

c)

2√7

d)

√17

24.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

25.

$5\sqrt{2}\cdot4\sqrt{10}$

a)

$20\sqrt{20}$

b)

$10\sqrt{40}$

c)

$40\sqrt{5}$

d)

$9\sqrt{13}$

26.

$\sqrt{6}\left(2\sqrt{6}\right)$

a)

12

b)

$12\sqrt{6}$

c)

$2\sqrt{36}$

d)

$\sqrt{72}$

27.

Simplify the expression:

a)

1

b)

9 - 4√4

c)

6 + 2√2

d)

1 - 4√2

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

What kind of function is represented by the graph?

a)

Cube Root Function

b)

Cubic Function

c)

Polynomial Function

d)

Square Root Function

34.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

35.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

36.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

37.

What is the Domain of ALL Cube Root Functions in interval notation?

a)

(−∞,∞)

b)

−∞<x<∞

c)

(−∞,0]

d)

All Cube Root Functions are different.

38.

What is the equation for the red function?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

39.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

40.

What are the shifts of the graph

f\left(x\right)=\left(x-2\right)^3-8

from the parent graph of

f\left(x\right)=x^3

?

a)

Left 2 and Up 8

b)

Right 2 and Up 8

c)

Left 2 and Down 8

d)

Right 2 and Down 8

41.

What are the shifts of the graph

f\left(x\right)=\left(x-15\right)^3+7

from the parent graph of

f\left(x\right)=x^3

?

a)

Left 15 and Up 7

b)

Right 15 and Up 7

c)

Left 15 and Down 7

d)

Right 15 and Down 7

42.

Which of the following is the graph of y = (x – 1)³ – 7?

a)

b)

c)

d)

43.

Simplify $\frac{\sqrt{c^5}}{\sqrt{d^9}}$

a)

$\frac{c^2\sqrt{cd}}{d^5}$

b)

$\frac{c^2}{d^4}$

c)

$\frac{c^2\sqrt{c}}{d^{4\sqrt{d}}}$

d)

$\frac{c}{d}\sqrt{\frac{c}{d}}$

44.

Only _____________________________ can be combined when adding and subtracting radicals.

a)

Like radical expressions

b)

Unlike radical expressions

c)

radicals with the same index

d)

radicals with different indexes.

45.

$a\sqrt{b}+c\sqrt{d}\ and\ a\sqrt{b}-c\sqrt{d}$ are _________________.

a)

Like radicals

b)

Conjugates

c)

Simplifed

d)

Principals

46.

Simplify $\frac{8}{\sqrt{6}-5}$

a)

$\frac{\left(-40-8\sqrt{6}\right)}{19}$

b)

$\frac{27-10\sqrt{3}}{13}$

c)

$40$

d)

$-2-\sqrt{2}$

47.

a)

A

b)

B

c)

C

d)

D

48.

What is the conjugate of $\sqrt{2}+2\sqrt{3}$

a)

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

b)

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

c)

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

49.

a)

A

b)

B

c)

C

d)

D

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

A

b)

B

c)

C

d)

D

53.

a)

A

b)

B

c)

C

d)

D

54.

Divide and simplify.

a)

4x√x

b)

3x²/x³√36

c)

2x

d)

4x²

55.

Rationalize the denominator.

a)

2x³

b)

(x√35x) / 5

c)

(x√7x) / 25

d)

49x⁷y / 5

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

Simplify.

a)

b)

c)

d)

60.

Simplify.

a)

b)

c)

d)

61.

Simplify.

a)

b)

c)

d)

62.

Simplify.

a)

b)

c)

d)

63.

Simplify.

a)

b)

c)

d)

Simplifying Radical Expressions Review

Total questions: 63

Worksheet time: 5hrs 15mins

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