Square 1 to 30
📚 Introduction to Squares from 1 to 30
Square numbers are created by multiplying a number by itself. For example, 7 × 7 = 49, so 49 is a square number. Learning squares from 1 to 30 helps students speed up mental calculations and solve geometry or algebra problems efficiently. Let’s explore the full list and helpful learning strategies!
🔢 Square Numbers from 1 to 30 (Complete List)
Here is the table of square numbers from 1 to 30:
| 1–10 | 11–20 | 21–30 |
|---|---|---|
| 1² = 1 | 11² = 121 | 21² = 441 |
| 2² = 4 | 12² = 144 | 22² = 484 |
| 3² = 9 | 13² = 169 | 23² = 529 |
| 4² = 16 | 14² = 196 | 24² = 576 |
| 5² = 25 | 15² = 225 | 25² = 625 |
| 6² = 36 | 16² = 256 | 26² = 676 |
| 7² = 49 | 17² = 289 | 27² = 729 |
| 8² = 64 | 18² = 324 | 28² = 784 |
| 9² = 81 | 19² = 361 | 29² = 841 |
| 10² = 100 | 20² = 400 | 30² = 900 |
🔷 Squares of Even Numbers (1 to 30)
Even numbers between 1 and 30 include: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
| Even Number | Square |
|---|---|
| 2 | 4 |
| 4 | 16 |
| 6 | 36 |
| 8 | 64 |
| 10 | 100 |
| 12 | 144 |
| 14 | 196 |
| 16 | 256 |
| 18 | 324 |
| 20 | 400 |
| 22 | 484 |
| 24 | 576 |
| 26 | 676 |
| 28 | 784 |
| 30 | 900 |
🔶 Squares of Odd Numbers (1 to 30)
Odd numbers between 1 and 30 include: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
| Odd Number | Square |
|---|---|
| 1 | 1 |
| 3 | 9 |
| 5 | 25 |
| 7 | 49 |
| 9 | 81 |
| 11 | 121 |
| 13 | 169 |
| 15 | 225 |
| 17 | 289 |
| 19 | 361 |
| 21 | 441 |
| 23 | 529 |
| 25 | 625 |
| 27 | 729 |
| 29 | 841 |
🧠 How to Calculate Square Numbers (Two Methods)
Method 1: Multiply the Number by Itself
The most direct way to find a square is by multiplying the number with itself.
Example:8 × 8 = 64
Method 2: Use Algebraic Identities
Break larger numbers into simpler expressions using algebraic identities like:
- (a + b)² = a² + 2ab + b²
- (a – b)² = a² – 2ab + b²
Example:Find the square of 29
→ 29 = (30 – 1)
→ (30)² – 2×30×1 + (1)² = 900 – 60 + 1 = 841
📐 Real-Life Applications: Solved Examples
✅ Example 1:
What’s the area of a circular rug with a radius of 16 inches?
Area = π × r² = π × 256 = approx. 804.25 in²
✅ Example 2:
What’s the area of a square window with side 25 inches?
Area = side² = 25² = 625 in²
✅ Example 3:
Two square tiles with sides 10 m and 12 m—what’s their total area?
Tile 1: 10² = 100 m²
Tile 2: 12² = 144 m²
Total = 244 m²
✅ Example 4:
Find the square of 15
Answer: 15² = 225
🎓 Final Thoughts
Learning and memorizing squares from 1 to 30 sharpens your math foundation and boosts your speed in problem-solving. Whether you’re preparing for exams, doing homework, or just curious about numbers, mastering square numbers is a skill worth having!
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