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Adding and Subtracting Radicals - Printable Mathematics Worksheets grade 11 - Wayground

Adding and Subtracting Radicals

11 questions

11th - 11th Grade

Mathematics

Adding and Subtracting Radicals is a Grade 11 mathematics worksheet that develops students’ ability to identify like radicals, simplify radical expressions, and combine radical terms correctly. The 11-question set includes 10 multiple-choice questions and one multiple-select question, with true-or-false checks about radical indices and radicands alongside problems involving square roots, cube roots, and addition or subtraction of like radicals. Students apply these skills to expressions such as subtracting identical radicals, combining cube-root terms, simplifying coefficients, and rewriting radicals such as √20, √75, and √300 before combining them. This free printable worksheet with an answer key is useful for guided practice, independent work, or a short Grade 11 skills check. Its varied question formats help teachers see whether students understand the definition of like radicals as well as whether they can carry out the simplification and combining steps accurately.

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Worksheets

Adding and Subtracting Radicals

Total questions: 11

Name
Class
Date
1.

1. You can combine radicals with different indices.

a)

TRUE

b)

FALSE

2.

Like radicals are radicals with the same indices and same radicands.

a)

TRUE

b)

FALSE

3.

56 + 8 6− 365\sqrt{6}\ +\ 8\ \sqrt{6}-\ 3\sqrt{6}  

a)

10610\sqrt{6}  

b)

16616\sqrt{6}  

c)

6\sqrt{6}  

4.

2 7 −5 72\ \sqrt{7}\ -5\ \sqrt{7}  

a)

373\sqrt{7}  

b)

−37-3\sqrt{7}  

c)

777\sqrt{7}  

5.

Simplify 

11√21 - 11√21

a)
0
b)

−22 21-22\ \sqrt[]{21}  

c)

21\sqrt[]{21}  

d)

42\sqrt[]{42}   

6.

(2∛4)+(7∛4)

a)

9∛8

b)

52

c)

9∛16

d)

9∛4

7.
Simplify
a)
√25
b)
5
c)
2√5
d)
√10
8.
Add:  4√7 - 10 √7 + 7√7
a)
-6√7
b)
14√7
c)
-3√14
d)
√7
9.
√5 + √20
a)
5
b)
25
c)
3√5
d)
2√3
10.
a)
13√3
b)
10√30
c)
13√6
d)
11√3
11.

√300 + √75

a)

15√3

b)

√375

c)

20√5

d)

16√5

Answer Key

Adding and Subtracting Radicals

Total questions: 11

1.
b)

FALSE

2.
a)

TRUE

3.
a)

10610\sqrt{6}  

4.
b)

−37-3\sqrt{7}  

5.
a) 0
6.
d)

9∛4

7.
c) 2√5
8.
d) √7
9.
c) 3√5
10.
a) 13√3
11.
a)

15√3

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FAQs

What does this Adding and Subtracting Radicals worksheet cover?

This Grade 11 worksheet focuses on identifying like radicals, simplifying square and cube roots, and adding or subtracting radical terms. Its 10 multiple-choice and one multiple-select question require students to distinguish matching indices and radicands, combine coefficients correctly, and simplify expressions such as √5 + √20 and √300 + √75.

How can I use this worksheet to teach adding and subtracting radicals?

Introduce the worksheet by having students identify the index and radicand in each radical, then model how to simplify each radicand before combining like terms. Use the cube-root item and the multi-term expression with √7 to discuss why only radicals with matching indices and radicands can be combined, and ask students to explain why an expression such as √5 + √20 must be simplified first.

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

Watch for students combining radicals with different indices, treating unlike radicands as like terms, or adding radicands instead of adding the coefficients. Students may also stop before simplifying √20, √75, or √300, mishandle the negative coefficient in 4√7 − 10√7 + 7√7, or change the radicand when combining cube-root terms.

How do I assign and grade this Adding and Subtracting Radicals worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for the 11 questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital version supports online completion and grading.

How can I differentiate this radicals worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the radical expressions and answer choices easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the square-root, cube-root, and like-radical practice intact.

Where can I find more worksheets like this on Wayground?

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

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