Mathematics is the foundation of logical thinking, and mastering Squares, Cubes, and Square Roots is essential for students from Class 6 to Class 10. These concepts form the building blocks for algebra, geometry, and higher-level mathematics. At Dhingra Classes Nashik, we emphasize concept-based learning and regular practice to help students excel in these fundamental topics.
This detailed worksheet listing is designed for Class 6 to 10 students and includes comprehensive tables of:
Squares of Numbers from 1 to 30
Cubes of Numbers from 1 to 15
Square Roots of Numbers from 1 to 10
Practice Exercises – Fill in the blanks, True/False, Match the following, Word problems
Answer Key – For all exercises
📘 Quick Revision – Squares, Cubes, and Square Roots
| Concept | Definition | Example |
|---|---|---|
| Square of a Number | A number multiplied by itself. | 5² = 5 × 5 = 25 |
| Perfect Square | A number whose square root is an integer. | 25, 36, 49 |
| Cube of a Number | A number multiplied by itself three times. | 3³ = 3 × 3 × 3 = 27 |
| Perfect Cube | A number whose cube root is an integer. | 8, 27, 64 |
| Square Root | The inverse operation of squaring. | √25 = 5 |
| Cube Root | The inverse operation of cubing. | ∛27 = 3 |
📊 Table 1: Squares of Numbers from 1 to 30
| Number | Square | Number | Square |
|---|---|---|---|
| 1 | 1 | 16 | 256 |
| 2 | 4 | 17 | 289 |
| 3 | 9 | 18 | 324 |
| 4 | 16 | 19 | 361 |
| 5 | 25 | 20 | 400 |
| 6 | 36 | 21 | 441 |
| 7 | 49 | 22 | 484 |
| 8 | 64 | 23 | 529 |
| 9 | 81 | 24 | 576 |
| 10 | 100 | 25 | 625 |
| 11 | 121 | 26 | 676 |
| 12 | 144 | 27 | 729 |
| 13 | 169 | 28 | 784 |
| 14 | 196 | 29 | 841 |
| 15 | 225 | 30 | 900 |
📊 Table 2: Cubes of Numbers from 1 to 15
| Number | Cube | Number | Cube |
|---|---|---|---|
| 1 | 1 | 9 | 729 |
| 2 | 8 | 10 | 1000 |
| 3 | 27 | 11 | 1331 |
| 4 | 64 | 12 | 1728 |
| 5 | 125 | 13 | 2197 |
| 6 | 216 | 14 | 2744 |
| 7 | 343 | 15 | 3375 |
| 8 | 512 | – | – |
📊 Table 3: Square Roots of Numbers from 1 to 10
| Number | Square Root |
|---|---|
| 1 | 1 |
| 2 | √2 ≈ 1.414 |
| 3 | √3 ≈ 1.732 |
| 4 | 2 |
| 5 | √5 ≈ 2.236 |
| 6 | √6 ≈ 2.449 |
| 7 | √7 ≈ 2.646 |
| 8 | √8 ≈ 2.828 |
| 9 | 3 |
| 10 | √10 ≈ 3.162 |
📝 Section A – Fill in the Blanks (10 Questions)
Instructions: Fill in the blanks with the correct answers.
| Question | Answer |
|---|---|
| 1. The square of 12 is ______. | 144 |
| 2. The cube of 7 is ______. | 343 |
| 3. √169 = ______. | 13 |
| 4. ∛64 = ______. | 4 |
| 5. The square root of 225 is ______. | 15 |
| 6. The cube root of 27 is ______. | 3 |
| 7. 18² = ______. | 324 |
| 8. 5³ = ______. | 125 |
| 9. √400 = ______. | 20 |
| 10. ∛1000 = ______. | 10 |
📝 Section B – True or False (10 Questions)
Instructions: Write True or False for the following statements.
| Question | Answer |
|---|---|
| 1. 14² = 196 | True |
| 2. 6³ = 216 | True |
| 3. √81 = 8 | False (√81 = 9) |
| 4. ∛125 = 5 | True |
| 5. 22² = 484 | True |
| 6. √144 = 14 | False (√144 = 12) |
| 7. 10³ = 1000 | True |
| 8. ∛216 = 6 | True |
| 9. 9² = 81 | True |
| 10. √625 = 25 | True |
📝 Section C – Match the Following (10 Questions)
Instructions: Match the numbers in Column A with their correct squares, cubes, square roots, or cube roots in Column B.
| Column A | Column B |
|---|---|
| 1. 15² | A. 729 |
| 2. 9³ | B. 225 |
| 3. √256 | C. 7 |
| 4. ∛343 | D. 16 |
| 5. 20² | E. 9 |
| 6. √81 | F. 400 |
| 7. 6³ | G. 5 |
| 8. √25 | H. 216 |
| 9. 13² | I. 169 |
| 10. ∛512 | J. 8 |
Answers:
15² → B (225)
9³ → A (729)
√256 → D (16)
∛343 → C (7)
20² → F (400)
√81 → E (9)
6³ → H (216)
√25 → G (5)
13² → I (169)
∛512 → J (8)
📝 Section D – Word Problems (5 Questions)
Question 1: A square garden has an area of 625 m². What is the length of one side?
Answer: Side = √625 = 25 m
Question 2: A cube has a volume of 729 cm³. What is the length of its edge?
Answer: Edge = ∛729 = 9 cm
Question 3: The area of a square is 144 cm². Find its perimeter.
Answer: Side = √144 = 12 cm; Perimeter = 4 × 12 = 48 cm
Question 4: A cubical tank has a volume of 1331 L. What is the length of its edge?
Answer: Edge = ∛1331 = 11 L
Question 5: A square field has a side of 18 m. What is its area?
Answer: Area = 18² = 324 m²
📝 Section E – Find the Square or Cube (10 Questions)
Instructions: Find the square or cube of the following numbers.
| Question | Answer |
|---|---|
| 1. 23² | 529 |
| 2. 8³ | 512 |
| 3. 29² | 841 |
| 4. 12³ | 1728 |
| 5. 26² | 676 |
| 6. 6³ | 216 |
| 7. 30² | 900 |
| 8. 13³ | 2197 |
| 9. 24² | 576 |
| 10. 9³ | 729 |
📝 Section F – Find the Square Root or Cube Root (10 Questions)
Instructions: Find the square root or cube root of the following numbers.
| Question | Answer |
|---|---|
| 1. √196 | 14 |
| 2. ∛512 | 8 |
| 3. √324 | 18 |
| 4. ∛216 | 6 |
| 5. √625 | 25 |
| 6. ∛1000 | 10 |
| 7. √1024 | 32 |
| 8. ∛343 | 7 |
| 9. √441 | 21 |
| 10. ∛729 | 9 |
📝 Section G – Identify the Type (10 Questions)
Instructions: Identify whether the following numbers are perfect squares, perfect cubes, both, or neither.
| Number | Type |
|---|---|
| 1. 64 | Perfect Square & Perfect Cube |
| 2. 81 | Perfect Square |
| 3. 125 | Perfect Cube |
| 4. 36 | Perfect Square |
| 5. 216 | Perfect Cube |
| 6. 100 | Perfect Square |
| 7. 27 | Perfect Cube |
| 8. 121 | Perfect Square |
| 9. 512 | Perfect Cube |
| 10. 49 | Perfect Square |
📝 Section H – Find the Square Using Identity (5 Questions)
Instructions: Use the identity (a + b)² = a² + 2ab + b² to find the square of the following.
| Question | Answer |
|---|---|
| 1. 21² | (20 + 1)² = 400 + 40 + 1 = 441 |
| 2. 19² | (20 – 1)² = 400 – 40 + 1 = 361 |
| 3. 22² | (20 + 2)² = 400 + 80 + 4 = 484 |
| 4. 18² | (20 – 2)² = 400 – 80 + 4 = 324 |
| 5. 15² | (10 + 5)² = 100 + 100 + 25 = 225 |
💡 Tips to Master Squares, Cubes, and Square Roots
| Tip | Description |
|---|---|
| Memorize Tables | Learn squares up to 30 and cubes up to 15. |
| Use Prime Factorization | Break numbers into prime factors for roots. |
| Check Last Digit | A perfect square never ends in 2, 3, 7, or 8. |
| Practice Daily | Solve at least 10 problems daily. |
| Use Identities | Apply (a ± b)² for quick calculations. |
How Dhingra Classes Helps Students Master Mathematics
At Dhingra Classes Nashik, we provide:
Conceptual teaching – Building strong fundamentals in Mathematics.
Regular practice – Worksheets, exercises, and mock tests.
Doubt-clearing sessions – Instant clarification of queries.
Personalized feedback – Identifying strengths and areas for improvement.
Contact Dhingra Classes
Phone: 98230 62106
Email: dhingraclassesnsk@gmail.com
Website: www.dhingraclassesnashik.com
Address: Plot No 3, XQ3G+H3M Deacon Homes, 301C, opp. Metro Zone, near Guru Govind Sing, Samarth Nagar, Dnyaneshwar Nagar, Pathardi Phata, Nashik, Maharashtra 422009
Conclusion
Mastering Squares, Cubes, and Square Roots is essential for students in Class 6 to 10 to build a strong foundation in Mathematics. This detailed worksheet listing provides comprehensive tables and practice exercises, helping students memorize and apply these concepts with ease.
At Dhingra Classes Nashik, we are committed to helping students achieve academic excellence through expert guidance and structured practice. Join us and embark on your journey to success!
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