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Class 8 Squares and Square Roots Worksheet

By Swati Singh

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Updated on 10 Apr 2026, 15:19 IST

Understanding squares and square roots is a key building block in mathematics that helps students solve problems faster and think more logically. From calculating areas to simplifying complex expressions, these concepts appear in everyday maths and higher-level topics alike.

This Class 8 Maths worksheet on Squares and Square Roots is designed to give students a strong foundation through structured practice. It covers everything from basic square calculations to finding square roots using different methods, along with real-life application-based questions.

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The worksheet is ideal for:

  • Reinforcing classroom learning
  • Practicing problem-solving skills
  • Preparing for exams with confidence

With a mix of straightforward questions and challenging problems, students can gradually improve accuracy and speed while developing a deeper understanding of the topic.

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Class 8 Maths – Squares and Square Roots Worksheet

Objective: Strengthen understanding of squares, square roots, and their applications through practice.

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Section A: Basic Concepts

  1. Find the squares of the following numbers:
    a) 12
    b) 25
    c) 37
    d) 48
  2. Fill in the blanks:
    a) 15² = ____
    b) √81 = ____
    c) 19² = ____
    d) √144 = ____
  3. Identify whether the following are perfect squares:
    a) 121
    b) 150
    c) 169
    d) 200

Section B: Square Roots

  1. Find the square roots:
    a) 64
    b) 225
    c) 400
    d) 529
  2. Find the square root using prime factorization:
    a) 196
    b) 324
    c) 441
  3. Estimate the square root (nearest integer):
    a) √50
    b) √90
    c) √130

Section C: Properties and Patterns

  1. Find the unit digit of the squares of:
    a) 23
    b) 47
    c) 89
  2. Without actual calculation, tell whether the square of the following numbers is odd or even:
    a) 34
    b) 57
    c) 90
  3. Find the smallest number that must be added to make the following a perfect square:
    a) 50
    b) 72
    c) 99

Section D: Word Problems

  1. A square garden has an area of 576 m². Find the length of one side.
  2. A number when multiplied by itself gives 784. Find the number.
  3. The area of a square floor is 1024 cm². Find the side of the floor.

Section E: Challenge Questions

  1. Find the least number by which 180 must be multiplied to make it a perfect square.
  2. Find the square root of 2025 using long division method.
  3. The product of two consecutive even numbers is 224. Find the numbers.

Answer Key (For Teachers/Parents)

Section A:
1. a) 144 b) 625 c) 1369 d) 2304
2. a) 225 b) 9 c) 361 d) 12
3. a) Yes b) No c) Yes d) No

Section B:
4. a) 8 b) 15 c) 20 d) 23
5. a) 14 b) 18 c) 21
6. a) 7 b) 9 c) 11

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Section C:
7. a) 9 b) 9 c) 1
8. a) Even b) Odd c) Even
9. a) 14 b) 9 c) 1

Section D:
10. 24 m
11. 28
12. 32 cm

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Section E:
13. 5
14. 45
15. 14 and 16

 Importance of Solving Class 8 Maths Worksheets

Solving Class 8 Maths worksheets plays a crucial role in building a strong mathematical foundation. At this stage, concepts like squares and square roots are not just theoretical—they require consistent practice to fully understand and apply.

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1. Strengthens Concept Clarity: Worksheets help students move beyond memorization. By solving a variety of questions, they gain a clear understanding of how concepts actually work.

2. Improves Problem-Solving Skills: Regular practice trains the brain to approach problems logically and efficiently, which is essential for higher-level maths.

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3. Boosts Speed and Accuracy: Timed worksheet practice helps students solve questions faster while reducing calculation mistakes—key for exams.

4. Builds Confidence for Exams: The more students practice, the more familiar they become with different question types, making exams less stressful.

5. Identifies Weak Areas: Worksheets act like a self-check tool. Students can easily spot topics they struggle with and focus on improving them.

6. Encourages Independent Learning: Solving worksheets regularly helps students become more self-reliant and disciplined in their studies.

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FAQs – Class 8 Maths Squares and Square Roots Worksheet

What is included in a Class 8 Squares and Square Roots worksheet?

It includes questions on finding squares, square roots, perfect squares, estimation, and word problems to help students practice the topic thoroughly.

Why is practicing squares and square roots important for Class 8 students?

It helps build strong calculation skills, improves accuracy, and forms the base for advanced maths topics like algebra and geometry

How can students easily learn square roots?

Students can learn square roots by practicing prime factorization, using estimation methods, and solving worksheets regularly.

Are these worksheets useful for exam preparation?

Yes, these worksheets cover important question types that are commonly asked in exams, helping students prepare effectively.

What are perfect squares in Class 8 Maths?

Perfect squares are numbers that are obtained by multiplying a number by itself, such as 1, 4, 9, 16, 25, etc.

How often should students practice these worksheets?

Students should practice at least 2–3 worksheets per week to improve speed, accuracy, and confidence.

Can worksheets help improve problem-solving skills?

Yes, regular worksheet practice helps students understand different types of problems and develop logical thinking skills.