Wayground
Algebra 2 Simplify Radicals - Printable Mathematics Worksheets - Wayground

Algebra 2 Simplify Radicals

15 questions

9th - 12th Grade

Mathematics

This Grade 9–12 mathematics worksheet gives students focused practice simplifying radical expressions. It contains 15 multiple-choice questions that ask learners to reduce radicals, including expressions with numerical coefficients and variables. Items such as 27m^7p^4 and 2√48 require students to identify perfect-power factors, extract them from the radical, and present the result in simplified form. Designed for Algebra 2 instruction, this free printable worksheet can support guided practice, independent work, review, or a quick check of procedural fluency. The repeated multiple-choice format lets teachers see whether students can apply radical-simplification rules consistently across numeric and algebraic expressions, while the answer choices can prompt discussion about common errors. A complete answer key is included for efficient checking and feedback.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Algebra 2 Simplify Radicals

Total questions: 15

Name
Class
Date
1.

Simplify the radical expression:
2x2y3\sqrt{2x^2y^3}  

a)

2yxy2y\sqrt{xy}  

b)

2xy22x\sqrt{y^2}  

c)

y2xyy\sqrt{2xy}  

d)

xy2yxy\sqrt{2y}  

2.

Simplify the radical expression:
128a3b4\sqrt{128a^3b^4}  

a)

8ab22a8ab^2\sqrt{2a}  

b)

2a8ab22a\sqrt{8ab^2}  

c)

2ab64ab2ab\sqrt{64ab}  

d)

64ab22a64ab^2\sqrt{2a}  

3.

Simplify the radical:
98\sqrt{98}  

a)

272\sqrt{7}  

b)

727\sqrt{2}  

c)

14214\sqrt{2}  

d)

49249\sqrt{2}  

4.

Simplify the radical:
180\sqrt{180}  

a)

565\sqrt{6}  

b)

555\sqrt{5}  

c)

13513\sqrt{5}  

d)

656\sqrt{5}  

5.

Simplify the radical expression:
27m7p4 \sqrt{27m^7p^{4\ }}

a)

3m3m3p23m\sqrt{3m^3p^2}

b)

3m3p23m3m^3p^2\sqrt{3m}

c)

9mp3m9mp\sqrt{3m}

d)

9m3p23m9m^3p^2\sqrt{3m}

6.

Simplify the radical expression:
x3y5z2\sqrt{x^3y^5z^2}  

a)

xy2zxy^2z  

b)

x2y4z2xyx^2y^4z^2\sqrt{xy}  

c)

xy2zxyxy^2z\sqrt{xy}  

d)

xyzxyxyz\sqrt{xy}  

7.

Simplify the radical expression:
151r2s3\sqrt{151r^2s^3}  

a)

rs151srs\sqrt{151s}  

b)

151rss151rs\sqrt{s}  

c)

10rs15s10rs\sqrt{15s}  

d)

r2s2151sr^2s^2\sqrt{151s}  

8.

Simplify the radical:
169\sqrt{169}  

a)

2132\sqrt{13}  

b)

13213\sqrt{2}  

c)

131313\sqrt{13}  

d)

1313  

9.

Simplify the radical expression:
2482\sqrt{48}

a)

434\sqrt{3}

b)

838\sqrt{3}

c)

232\sqrt{3}

d)

383\sqrt{8}

10.

Simplify the radical expression:
92a2b3\sqrt{92a^2b^3}  

a)

23ab2b23ab\sqrt{2b}  

b)

2ab23b2ab\sqrt{23b}  

c)

4ab23b4ab\sqrt{23b}  

d)

4a2b223b4a^2b^2\sqrt{23b}  

11.

Simplify the radical expression:
289c5\sqrt{289c^5}  

a)

17c2c17c^2\sqrt{c}  

b)

17c417c17c^4\sqrt{17c}  

c)

28c29c28c^2\sqrt{9c}  

d)

34c2c34c^2\sqrt{c}  

12.

Simplify the radical:
71247\sqrt{124}  

a)

2312\sqrt{31}  

b)

7317\sqrt{31}  

c)

143114\sqrt{31}  

d)

283128\sqrt{31}  

13.

Simplify the radical expression:
63x2y5\sqrt{63x^2y^5}  

a)

3xy27y3xy^2\sqrt{7y}  

b)

9xy7y9xy\sqrt{7y}  

c)

3y7xy23y\sqrt{7xy^2}  

d)

7y29xy7y^2\sqrt{9xy}  

14.

Simplify the radical:
190\sqrt{190}  

a)

101910\sqrt{19}  

b)

191019\sqrt{10}  

c)

2952\sqrt{95}  

d)

190\sqrt{190}  

15.

Simplify the radical expression:
256a2b22\sqrt{56a^2b^2}  

a)

4ab144ab\sqrt{14}  

b)

2ab142ab\sqrt{14}  

c)

14ab2ab14ab\sqrt{2ab}  

d)

142ab14\sqrt{2ab}  

Answer Key

Algebra 2 Simplify Radicals

Total questions: 15

1.
d)

xy2yxy\sqrt{2y}  

2.
a)

8ab22a8ab^2\sqrt{2a}  

3.
b)

727\sqrt{2}  

4.
d)

656\sqrt{5}  

5.
b)

3m3p23m3m^3p^2\sqrt{3m}

6.
c)

xy2zxyxy^2z\sqrt{xy}  

7.
a)

rs151srs\sqrt{151s}  

8.
d)

1313  

9.
b)

838\sqrt{3}

10.
b)

2ab23b2ab\sqrt{23b}  

11.
a)

17c2c17c^2\sqrt{c}  

12.
c)

143114\sqrt{31}  

13.
a)

3xy27y3xy^2\sqrt{7y}  

14.
d)

190\sqrt{190}  

15.
a)

4ab144ab\sqrt{14}  

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Algebra 2 Simplify Radicals worksheet cover?

This worksheet covers simplifying radical expressions by identifying perfect-power factors and moving them outside the radical. Its 15 multiple-choice items include both numerical and variable expressions, such as 2√48 and √(27m^7p^4), so students practise applying the same simplification process across different forms.

How can I use this worksheet to teach students to simplify radical expressions?

Model a consistent process before students begin: factor the radicand, identify factors with exponents that can leave the radical, and rewrite the expression in simplified form. Then use the multiple-choice options to discuss why an unsimplified radical, an incorrectly extracted factor, or a misplaced coefficient is not equivalent to the correct result.

What mistakes should I watch for when students complete this radical simplification worksheet?

Watch for students who leave perfect-power factors under the radical, treat a coefficient such as the 2 in 2√48 as part of the radicand, or simplify numerical and variable factors inconsistently. In expressions such as √(27m^7p^4), students may also overlook how exponents determine which factors can be extracted.

How do I assign and grade the Algebra 2 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. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz.

How can I differentiate this worksheet for students who need support with radical expressions?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the 15 multiple-choice radical items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options help students access the instructions and answer choices.

Where can I find more free worksheets like this on Wayground?

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

© 2026 Wayground Inc.

Accessibility and Inclusion