Which Numbers 1 to 40 Are Perfect Squares?
The concept of Square 1 to 40 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Learning and memorizing the squares of numbers from 1 to 40 provides a strong base for calculations in competitive exams, quick mental maths, and understanding further mathematical concepts. This knowledge is especially useful for students aiming to improve their speed and accuracy in mathematics.
Understanding Square 1 to 40
A square number is the result of multiplying a number by itself. For example, the square of 7 is 49, because 7 × 7 = 49. The list of squares from 1 to 40 includes all the perfect squares between 1² and 40². This concept is widely used in square roots, finding perfect squares, and solving quadratic equations. Square numbers also help in geometry, area calculation, and pattern recognition tasks.
Formula Used in Square 1 to 40
The standard formula to calculate the square of any number ‘n’ is: \( n^2 = n \times n \)
Here’s a helpful table to understand Square 1 to 40 more clearly:
Square 1 to 40 Table
| Number (n) | Square (n × n) | In Words |
|---|---|---|
| 1 | 1 | One |
| 2 | 4 | Four |
| 3 | 9 | Nine |
| 4 | 16 | Sixteen |
| 5 | 25 | Twenty-five |
| 6 | 36 | Thirty-six |
| 7 | 49 | Forty-nine |
| 8 | 64 | Sixty-four |
| 9 | 81 | Eighty-one |
| 10 | 100 | One hundred |
| 11 | 121 | One hundred twenty-one |
| 12 | 144 | One hundred forty-four |
| 13 | 169 | One hundred sixty-nine |
| 14 | 196 | One hundred ninety-six |
| 15 | 225 | Two hundred twenty-five |
| 16 | 256 | Two hundred fifty-six |
| 17 | 289 | Two hundred eighty-nine |
| 18 | 324 | Three hundred twenty-four |
| 19 | 361 | Three hundred sixty-one |
| 20 | 400 | Four hundred |
| 21 | 441 | Four hundred forty-one |
| 22 | 484 | Four hundred eighty-four |
| 23 | 529 | Five hundred twenty-nine |
| 24 | 576 | Five hundred seventy-six |
| 25 | 625 | Six hundred twenty-five |
| 26 | 676 | Six hundred seventy-six |
| 27 | 729 | Seven hundred twenty-nine |
| 28 | 784 | Seven hundred eighty-four |
| 29 | 841 | Eight hundred forty-one |
| 30 | 900 | Nine hundred |
| 31 | 961 | Nine hundred sixty-one |
| 32 | 1024 | One thousand twenty-four |
| 33 | 1089 | One thousand eighty-nine |
| 34 | 1156 | One thousand one hundred fifty-six |
| 35 | 1225 | One thousand two hundred twenty-five |
| 36 | 1296 | One thousand two hundred ninety-six |
| 37 | 1369 | One thousand three hundred sixty-nine |
| 38 | 1444 | One thousand four hundred forty-four |
| 39 | 1521 | One thousand five hundred twenty-one |
| 40 | 1600 | One thousand six hundred |
This table shows how the pattern of Square 1 to 40 appears regularly in real cases and helps in calculations and finding square roots easily.
How to Calculate Squares from 1 to 40
There are simple ways to find square numbers quickly:
1. Multiply the number by itself. For example, square of 18 is 18 × 18 = 324.2. Use algebraic identities. For example, to find 23², write 23 as 20 + 3 and use (a + b)² = a² + 2ab + b²:
3. Learn patterns for ending digits. For example, numbers ending in 5 always have squares ending in 25.
4. Practice with square number tables like the one above for fast recall in exams.
Worked Example – Solving a Problem
1. What is the area of a square playground if one side is 24 metres?Step 2: Substitute side = 24.
Step 3: Area = 24 × 24 = 576.
Step 4: Final answer: The area is 576 square metres.
2. Find the square root of 529.
Step 2: 23 × 23 = 529.
Step 3: So, √529 = 23.
Practice Problems
Try the following for extra practice with square numbers:
1. List all square numbers from 10 to 30.2. Is 1225 a perfect square?
3. What is the square of 37?
4. Which numbers between 32 and 40 are perfect squares?
Common Mistakes to Avoid
- Confusing square numbers with multiplying a number by 2 instead of itself.
- Forgetting to write square numbers in words correctly during exams.
- Calculating area incorrectly by not squaring the length.
Real-World Applications
The concept of Square 1 to 40 appears in areas such as area calculation (finding the surface of a square/rectangle), computer graphics, and pattern making. Bankers use square numbers for calculating interest, while engineers use them in construction design. Vedantu helps students see how maths applies beyond the classroom and in competitive exams.
We explored the idea of Square 1 to 40, how to calculate it, step-by-step solutions, practice problems, and its use in real-life maths. Practice more with Vedantu to build confidence in squares for exams and everyday applications.
Further Learning on Squares and Square Roots
- Square Numbers
- Squares and Square Roots
- Square Root Table from 1 to 50
- Square Root: Concept & Methods
- Square Root Prime Factorization
- Square Root Symbol
- Square Root of 1
- Square Root of 4
- Square Root of 9
- Square Root by Repeated Subtraction
FAQs on List of Squares and Square Roots for Numbers 1–40
1. What are the squares of numbers from 1 to 40?
The squares of numbers from 1 to 40 are obtained by multiplying each number by itself. They are:
1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225, 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400, 21² = 441, 22² = 484, 23² = 529, 24² = 576, 25² = 625, 26² = 676, 27² = 729, 28² = 784, 29² = 841, 30² = 900, 31² = 961, 32² = 1024, 33² = 1089, 34² = 1156, 35² = 1225, 36² = 1296, 37² = 1369, 38² = 1444, 39² = 1521, 40² = 1600.
2. What is the sum of numbers from 1 to 40?
The sum of numbers from 1 to 40 can be calculated using the formula n(n + 1)/2 where n = 40. Therefore, 40 × 41 / 2 = 820. The sum is 820.
3. Which square roots go into 40?
The square roots that go into 40 are the whole numbers whose squares are less than or equal to 40. These are 1, 2, 3, 4, 5, and 6 since 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, and 6² = 36. So, square roots from 1 to 6 go into 40. The square root of 40 is an irrational number, approximately 6.32.
4. How many perfect squares are there from 1 to 40?
The perfect squares from 1 to 40 are numbers that are squares of whole numbers within this range. These are: 1 (1²), 4 (2²), 9 (3²), 16 (4²), 25 (5²), and 36 (6²). So, there are 6 perfect squares between 1 and 40.
5. What are the cubes of numbers from 1 to 40?
The cubes of numbers from 1 to 40 are obtained by multiplying each number by itself twice (n × n × n). For example, 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, ..., 40³ = 64,000. These help in understanding exponents and number patterns.
6. What is the value of the square root of 40?
The square root of 40 is approximately 6.3246. It is an irrational number and can be written exactly as √40 or simplified as 2√10.
7. What are perfect cubes between 1 and 40?
Perfect cubes between 1 and 40 are numbers raised to the power of 3. These are: 1 (1³), 8 (2³), 27 (3³). Therefore, there are 3 perfect cubes in this range.
8. Where can I download the square of 1 to 40 in PDF?
You can download a PDF of squares from 1 to 40 on many educational websites like Vedantu, BYJU'S, or other reliable learning platforms. Just search for 'Square of 1 to 40 PDF free download' to access the printable file for quick reference.
9. What are the uses of learning squares and cubes from 1 to 40?
Learning squares and cubes from 1 to 40 helps students solve mathematical problems quickly, prepare for exams, understand algebraic concepts, and improve mental calculation skills. It's essential for quick computations in competitive exams and higher mathematics.
10. What is the square root of numbers from 1 to 40?
The square roots of numbers from 1 to 40 include both exact roots for perfect squares (like √1 = 1, √4 = 2, ..., √36 = 6) and decimal approximations for non-squares (like √2 ≈ 1.41, √3 ≈ 1.73, etc.). Learning these assists with simplifying expressions and problem-solving.
11. How many 2-digit numbers are perfect squares from 1 to 40?
Among numbers from 1 to 40, the two-digit perfect squares are 9 (3²), 16 (4²), 25 (5²), and 36 (6²). Thus, there are 4 two-digit perfect squares in this range.
12. How can I use a squares and cubes worksheet for practice?
Squares and cubes worksheets can be used to practice calculation skills, recognize numerical patterns, and enhance familiarity with multiplication and exponents. Regular practice with these worksheets helps students remember values and perform faster calculations in exams and daily math tasks.
