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perfect squares and estimating square roots - Printable Mathematics Worksheets year 8 - Wayground

perfect squares and estimating square roots

20 questions

8th - 8th Grade

Mathematics

This free printable Grade 8 mathematics worksheet helps students connect perfect squares with their square roots and estimate the square roots of non-perfect squares. Across 20 questions, students identify squares such as 5², 11², √64, and √100; match perfect squares to their roots; determine which whole numbers bound a square root; compare a decimal with a square root; and identify the point representing a square root. The worksheet includes 17 multiple-choice questions, one matching item, one dropdown item, and one math-response item. Students use familiar perfect squares as benchmarks to estimate values such as √69, √20, and √27, building number-sense rather than relying only on memorized facts. It is suitable for Grade 8 instruction, guided practice, independent work, or a quick check of understanding. The worksheet is available as a free printable PDF and includes a complete answer key for efficient review and grading.

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perfect squares and estimating square roots

Total questions: 20

Name
Class
Date
1.
52
a)
16
b)
25
c)
20
d)
10
2.

Which number is √69 closest to?

a)

6

b)

7

c)

8

d)

9

e)

10

3.
Estimate the square root.

Estimate the square root.

a)

5.8

b)

5.4

c)

4.8

d)

5.0

4.
Estimate the square root.

Estimate the square root.

a)

7.4

b)

23

c)

6.8

d)

4.6

e)

6.2

5.

Match the following numbers to their square roots.

49

7

64

8

81

9

36

6

25

5

6.
Estimate the square root.

Estimate the square root.

a)

6.4

b)

5.8

c)

7.1

d)

6.9

7.
Which number has a square root that is between 5 and 6?

Which number has a square root that is between 5 and 6?

a)

48

b)

81

c)

28

d)

36

e)

20

8.
Estimate the square root.

Estimate the square root.

a)

3.2

b)

5.2

c)

4.8

d)

4.2

9.

Compare with <, >, and =.

2.5 ______ √8

a)

<

b)

>

c)

=

10.
Between which two whole numbers is the √20 ?

Between which two whole numbers is the

√20 ?

a)

5 and 6

b)

10 and 2

c)

4 and 5

d)

3 and 4

11.
√ 64
a)
4
b)
6
c)
9
d)
8
12.
Which point best represents √27?

Which point best represents √27?

a)

point A

b)

point B

c)

point C

d)

point D

e)

point E

13.
Question Image
a)

a

b)

b

c)

c

d)

d

14.
22
a)
2
b)
4
c)
5
d)
6
15.
112
a)
132
b)
144
c)
121
d)
22
16.
√100
a)
15
b)
10
c)
11
d)
12
17.
Which of the following is NOT a perfect square?
a)
1
b)
4
c)
100
d)
8
18.

A perfect square is​ the​ (a)   of an integer and itself.

Choose from the below words
product
sum
difference
quotient
19.
In between what two integers is the square root of 44?
a)
3 and 4
b)
4 and 5
c)
5 and 6
d)
6 and 7
20.

Solve.

(−5)2=\left(-5\right)^2=

WaygroundAnswer Key

perfect squares and estimating square roots

Total questions: 20

1.
b) 25
2.
c)

8

3.
b)

5.4

4.
c)

6.8

5.

49

 - 

7

, 

64

 - 

8

, 

81

 - 

9

, 

36

 - 

6

, 

25

 - 

5

6.
a)

6.4

7.
c)

28

8.
d)

4.2

9.
a)

<

10.
c)

4 and 5

11.
d) 8
12.
d)

point D

13.
c)

c

14.
b) 4
15.
c) 121
16.
b) 10
17.
d) 8
18.
product
19.
d) 6 and 7
20.

2525

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FAQs

What does this perfect squares and estimating square roots worksheet help students learn?

This Grade 8 worksheet develops students’ ability to identify perfect squares and their roots, then estimate non-perfect square roots by locating them between consecutive whole numbers or known square values. Its 20 items use multiple choice, matching, dropdown, and math-response formats to practise skills such as comparing 2.5 with √8, bounding √20, and selecting the point that represents √27.

How can I use this worksheet to teach estimating square roots?

Begin by reviewing nearby perfect squares and having students explain why a number such as 20 lies between 4² and 5². Then model how those benchmarks establish the whole-number bounds for √20 before students complete the worksheet’s estimation, comparison, matching, and point-identification items. Ask students to justify an estimate by naming the two perfect squares they used rather than choosing an answer from the options without explanation.

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

Watch for students confusing a number with its square root, such as selecting 64 instead of 8 for √64, or treating 11² as 22 rather than 121. Students may also reverse the bounds for a root, choose 5 and 6 for a number whose root is between 4 and 5, or compare a decimal with √8 without first estimating √8. In the matching and point-identification items, check that they use the square-root relationship rather than matching by the size of the numbers alone.

How do I assign and grade this perfect squares and estimating square roots worksheet?

Wayground provides this worksheet as both a printable PDF and a digital quiz, so you can assign the format that fits your Grade 8 math lesson. It includes a complete answer key for the 17 multiple-choice items and the matching, dropdown, and math-response items. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade responses efficiently.

How can I differentiate this square roots worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the square-root expressions, answer choices, and matching items are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while retaining its perfect-square and estimation tasks. These options let you create a more readable version of the same worksheet file without changing the mathematical practice.

Where can I find more free 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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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