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Algebra 1 Simplify Radicals (graded) 24.25 - Printable Mathematics Worksheets - Wayground

Algebra 1 Simplify Radicals (graded) 24.25

35 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet gives students focused practice simplifying square and cube radicals. Across 35 questions—32 multiple-choice items, one math-response item, and two multiple-select items—students simplify numerical radicals such as √150 and √28, extract perfect-square factors from expressions with variables, and rewrite cube roots such as ∛375 in simplest form. Several items ask students to identify equivalent expressions or determine which radicals are already in simplest form. The worksheet is useful for introducing, reinforcing, or checking students’ ability to recognize perfect-power factors, simplify coefficients and variable exponents, and preserve any remaining factor under the radical. Its varied response formats provide both selected-response practice and opportunities for students to produce or evaluate a simplified expression. This is a free printable worksheet with a complete answer key for Grade 8 math instruction, independent practice, homework, or review.

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Algebra 1 Simplify Radicals (graded) 24.25

Total questions: 35

Name
Class
Date
1.
Simplify 4√75
a)
4√5
b)
12√5
c)
20√3
d)
7√3
2.
Simplify the following radical: √150
a)
5√15
b)
5√2
c)
5√6
d)
15√5
3.

Simplify.


72\sqrt{72}  

a)

797\sqrt{9}  

b)

464\sqrt{6}  

c)

626\sqrt{2}  

d)

343\sqrt{4}  

4.
Simplify the radical...
√20a²b⁴
a)
2ab²√5
b)
4ab²√5
c)
5ab²√2
d)
2a²b²√5
5.

The expression x33\sqrt{x^{33}}  is equivalent to 

a)

x16xx^{16}\sqrt{x}  

b)

x4xx^4\sqrt{x}  

c)

x8xx^8\sqrt{x}  

d)

x2xx^2\sqrt{x}  

6.
5√48x²
a)
10x√3
b)
15x√3
c)
20x√3
d)
25x√3
7.
√36x³y⁴
a)
6y²x√x
b)
3y²√2x
c)
3y√x
d)
6x√3y
8.

Simplify 320\sqrt[]{320}

9.
√28m⁴n³
a)
m²n√7n
b)
7m²n√n
c)
2m²n√7n
d)
7m²n²√n
10.

Simplify the radical:

32x3\sqrt{32x^3}  

a)

8x4x8x\sqrt{4x}  

b)

16x16x  

c)

16xx16x\sqrt{x}  

d)

4x2x4x\sqrt{2x}  

11.

√28 =

a)

7√2

b)

7√4

c)

4√7

d)

2√7

12.

Which is equivalent to ∛375 in simplest form?

a)

3∛5

b)

5∛25

c)

3∛125

d)

5∛3

13.

What number can be written under the radical to make a true statement?

a)

405

b)

18,225

c)

3,645

d)

45

14.

√18 =

a)

3√2

b)

9√2

c)

3√9

d)

2√3

15.

Identify each expression that is in simplest radical form.

a)

∛27

b)

∛4

c)

∛3

d)

∛81

e)

∛96

16.
∛32
a)
4∛2
b)
2∛4
c)
2
d)
Simplified
17.

Which is equivalent to ∛54 in simplest form?

a)

3∛6

b)

9∛2

c)

3∛2

d)

3∛3

18.

Which statement is NOT true?

a)

√169 = 13

b)

152 = 225

c)

42 = √16

d)

√64 = 8

19.

What is the largest perfect square that goes into 96\sqrt{96}  ?

a)

4

b)

9

c)

6

d)

16

20.
The number under the radical sign or square root sign  is called the ______.
a)
radical sign
b)
radicand
c)
factor
d)
exponent
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.

∛1 =

a)

4

b)

3

c)

2

d)

1

25.

Identify each expression that is in simplest radical form.

a)

∛27

b)

∛50

c)

∛3

d)

∛81

e)

∛96

26.

(23)(45)\left(2\sqrt{3}\right)\left(4\sqrt{5}\right)  

a)

8158\sqrt{15}  

b)

12212\sqrt{2}  

c)

6156\sqrt{15}  

d)

16216\sqrt{2}  

27.

(1681)  = ?\sqrt{\left(\frac{16}{81}\right)}\ \ =\ ?  

a)

827\frac{8}{27}  

b)

89\frac{8}{9}  

c)

49\frac{4}{9}  

d)

43\frac{4}{3}  

28.

Solve for x when x3=18x^3=\frac{1}{8}  

a)

2

b)

164\frac{1}{64}  

c)

13\frac{1}{3}  

d)

12\frac{1}{2}  

29.

Select the set with all perfect squares.

a)

-144, 9, 50, 75, 81, 100

b)

9, 50, 81, 100

c)

9, 50, 75, 81, 100

d)

9, 81, 100

30.

Which of the following is irrational?

a)

49\sqrt{49}

b)

50\sqrt{50}

c)

81\sqrt{81}

d)

121\sqrt{121}

31.

Solve & simplify: ∛25 • ∛35

a)

7∛2

b)

7∛5

c)

15∛7

d)

5∛7

32.

192k7q8\sqrt{192k^7q^8}  

a)

8q43k78q^4\sqrt{3k^7}  

b)

8k3q438k^3q^4\sqrt{3}  

c)

8k3q43k8k^3q^4\sqrt{3k}  

d)

8k7q83k8k^7q^8\sqrt{3k}  

33.
√96p⁹
a)
4p³
b)
4p⁴√p
c)
4p⁴√6p
d)
4p⁴√2p
34.

4x7y5z9\sqrt{4x^7y^5z^9}  Simplify

a)

2x3y2z3xy2x^3y^2z^3\sqrt{xy}  

b)

2z3x7y52z^3\sqrt{x^7y^5}  

c)

2xyzx6y5z82xyz\sqrt{x^6y^5z^8}  

d)

2x3y2z4xyz2x^3y^2z^4\sqrt{xyz}  

35.
a)

A

b)

B

c)

C

d)

D

Answer Key

Algebra 1 Simplify Radicals (graded) 24.25

Total questions: 35

1.
c) 20√3
2.
c) 5√6
3.
c)

626\sqrt{2}  

4.
a) 2ab²√5
5.
a)

x16xx^{16}\sqrt{x}  

6.
c) 20x√3
7.
a) 6y²x√x
8.

858\sqrt{5}

9.
c) 2m²n√7n
10.
d)

4x2x4x\sqrt{2x}  

11.
d)

2√7

12.
d)

5∛3

13.
c)

3,645

14.
a)

3√2

15.
c)

∛3

, b)

∛4

16.
b) 2∛4
17.
c)

3∛2

18.
c)

42 = √16

19.
d)

16

20.
b) radicand
21.
c) C
22.
a) A
23.
b) B
24.
d)

1

25.
c)

∛3

, b)

∛50

26.
a)

8158\sqrt{15}  

27.
c)

49\frac{4}{9}  

28.
d)

12\frac{1}{2}  

29.
d)

9, 81, 100

30.
b)

50\sqrt{50}

31.
d)

5∛7

32.
c)

8k3q43k8k^3q^4\sqrt{3k}  

33.
c) 4p⁴√6p
34.
d)

2x3y2z4xyz2x^3y^2z^4\sqrt{xyz}  

35.
d)

D

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FAQs

What does this simplify radicals worksheet cover?

This Grade 8 worksheet focuses on simplifying square and cube radicals, including numerical expressions and radicals containing variables. Its 32 multiple-choice questions, one math-response item, and two multiple-select items require students to extract perfect-square or perfect-cube factors, simplify coefficients and variables, identify equivalent expressions, and recognize radicals already in simplest form.

How can I use this worksheet to teach students to simplify radicals?

Begin by modeling how to factor a radicand into a perfect square or cube and a remaining factor, then apply the same process to expressions with variables such as √20a²b⁴. Use the multiple-choice items to discuss why distractors leave a factor unsimplified or extract the wrong coefficient, and finish with the math-response and multiple-select items as opportunities for students to explain or compare simplified forms.

What mistakes should I watch for when students complete this simplifying radicals worksheet?

Watch for students choosing a factorization that is not a perfect square or cube, leaving a numerical factor under the radical when it can be extracted, or changing the radicand incorrectly while simplifying expressions such as √36x³y⁴. Students may also mishandle variable exponents, confuse square-root and cube-root simplification, or select an expression that is equivalent but not in simplest radical form.

How do I assign and grade this simplify radicals worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 35 questions. For printable submissions, scan student work with the Wayground for Teachers app to support grading and review.

How can I differentiate this simplifying radicals worksheet for my students?

Under the worksheet’s Advanced Settings, adjust font spacing and font size to make the radical expressions and answer choices easier to read, or enable a dyslexia-friendly font. You can also translate the worksheet into another language while keeping the numerical and variable radical problems intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students build essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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