How to Find the Cube of a Number Easily?
The concept of cubes from 1 to 50 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Memorizing cube numbers list helps students tackle problems in arithmetic, algebra, and quantitative aptitude quickly and accurately.
What Is Cubes From 1 to 50?
A cube number is the result of multiplying a number by itself three times (n × n × n or n3). For example, the cube of 4 is 4 × 4 × 4 = 64. Cubes from 1 to 50 represent the cube values for all natural numbers between 1 and 50. You’ll find this concept applied in areas such as Cubes and Cube Roots, solving volumetric word problems, and identifying number patterns in algebra.
Key Formula for Cubes From 1 to 50
Here’s the standard formula for the cube of a number:
\( n^3 = n \times n \times n \)
Where n is any whole number. To find cube numbers, just multiply the number by itself twice more.
Cubes From 1 to 50 Table (Printable)
Below is a complete cube table from 1 to 50 to help you revise quickly. You can use this as reference during last-minute exam prep.
| Number | Cube (n3) |
|---|---|
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
| 11 | 1331 |
| 12 | 1728 |
| 13 | 2197 |
| 14 | 2744 |
| 15 | 3375 |
| 16 | 4096 |
| 17 | 4913 |
| 18 | 5832 |
| 19 | 6859 |
| 20 | 8000 |
| 21 | 9261 |
| 22 | 10648 |
| 23 | 12167 |
| 24 | 13824 |
| 25 | 15625 |
| 26 | 17576 |
| 27 | 19683 |
| 28 | 21952 |
| 29 | 24389 |
| 30 | 27000 |
| 31 | 29791 |
| 32 | 32768 |
| 33 | 35937 |
| 34 | 39304 |
| 35 | 42875 |
| 36 | 46656 |
| 37 | 50653 |
| 38 | 54872 |
| 39 | 59319 |
| 40 | 64000 |
| 41 | 68921 |
| 42 | 74088 |
| 43 | 79507 |
| 44 | 85184 |
| 45 | 91125 |
| 46 | 97336 |
| 47 | 103823 |
| 48 | 110592 |
| 49 | 117649 |
| 50 | 125000 |
For a downloadable cubes from 1 to 50 PDF chart and for practice, you can visit the Cubes and Cube Roots page on Vedantu.
How to Find the Cube of a Number
To get the cube of any number from 1 to 50, use these steps:
1. Write the number.2. Multiply it by itself: n × n.
3. Multiply that result by the original number again: (n × n) × n.
4. The answer is the cube.
Example:
Cube of 8:
8 × 8 = 6464 × 8 = 512
So, 83 = 512.
Speed Trick or Shortcut for Cubes
Here's a quick trick to mentally find cubes of two-digit numbers (using the binomial expansion):
If you want to find the cube of (a + b): Use the formula:
(a + b)3 = a3 + 3a2b + 3ab2 + b3
Example: Cube of 12 (where a=10, b=2):
103 + 3×102×2 + 3×10×22 + 23 = 1000 + 600 + 120 + 8 = 1728Such tricks make math much easier, especially under time pressure in exams like NTSE, JEE, or Olympiads.
Cubes vs Cube Roots
A cube is multiplying a number by itself three times. A cube root is the opposite: finding a number which, when cubed, equals the given number. If you’re interested, you can check out the complete Cube Root Table page for roots from 1 to 50.
Cross-Disciplinary Usage
Cubes from 1 to 50 are not only useful in Maths but also play an important role in Physics, Computer Science, and logical reasoning. You’ll see cube numbers in formulas for volume, programming loops, and many exam questions. Students preparing for JEE or NEET often need quick recall of these values.
Try These Yourself
- What is the cube of 17?
- Check if 18 is a perfect cube.
- Find all cube numbers between 2000 and 10000.
- Name one number between 1 and 50 whose cube is also a square.
Frequent Errors and Misunderstandings
- Mixing up cubes with squares (n2 vs. n3).
- Multiplying the number only twice instead of three times.
- Not checking for calculation accuracy in larger numbers.
Relation to Other Concepts
The idea of cubes from 1 to 50 connects closely with topics such as square numbers, cube as a shape, and squares and cubes in sequence patterns. Mastering this helps students with roots, exponents, and advanced algebra.
Classroom Tip
A fast way to memorize cube numbers: Notice the ending digits pattern—cubes of numbers ending in 2 always end in 8; cubes ending in 4 always end in 4. Teachers at Vedantu use such tips for easy recall in live sessions.
We explored cubes from 1 to 50—from definition, formula, cube table, tricks, and links to related topics. Continue practicing with Vedantu to become fast in calculations and succeed in your exams!
Cubes and Cube Roots | Cube Root Table | Square Numbers | Cube (Concept & Shape)
FAQs on Cubes from 1 to 50: Meaning, Formula, Table & Tricks
1. What are cubes from 1 to 50 in maths?
In mathematics, cubes from 1 to 50 are the results of cubing each whole number from 1 to 50. This means multiplying each number by itself three times (n³). For example, the cube of 5 (5³) is 5 × 5 × 5 = 125.
2. How do you calculate the cube of a number?
To calculate the cube of a number, you multiply the number by itself three times. For example, to find the cube of 7, you calculate 7 × 7 × 7 = 343. The cube of a number n is denoted as n³.
3. What is the formula for finding the cube of a number?
The formula for finding the cube of a number n is simply n³ = n × n × n. This means you multiply the number by itself twice.
4. What are some easy ways to remember cubes?
Memorizing a cube table is helpful. You can also look for patterns and relationships between numbers. Practice regularly, and try using mental math techniques to improve your speed and accuracy.
5. What is the difference between a cube and a square?
A square is the result of multiplying a number by itself once (n²), while a cube is the result of multiplying a number by itself twice (n³). For example, the square of 4 is 16 (4 × 4), and the cube of 4 is 64 (4 × 4 × 4).
6. What is a perfect cube?
A perfect cube is a number that can be obtained by cubing a whole number. In other words, it's a number that has an exact cube root which is a whole number. For example, 27 is a perfect cube because 3 × 3 × 3 = 27.
7. How are cubes used in real-life situations?
Cubes are used extensively in various fields:
- Geometry: Calculating the volume of a cube-shaped object.
- Physics: In various formulas involving volume and three-dimensional space.
- Engineering: Design and construction.
8. What is the cube of 12?
The cube of 12 (12³) is 1728 (12 × 12 × 12 = 1728).
9. What is the cube of 25?
The cube of 25 (25³) is 15625 (25 × 25 × 25 = 15625).
10. Are there any tricks for calculating cubes quickly?
Yes, several mental math techniques can help. These include using difference of cubes, recognizing patterns, and using binomial expansion for larger numbers. Practice is key to mastering these techniques.
11. How can I download a table of cubes from 1 to 50?
A downloadable PDF of a cube table is available [link to PDF here]. This provides a handy reference for quick lookups during study or exam preparation.
12. What is the relationship between cubes and cube roots?
Cube roots are the inverse operation of cubing a number. If n³ = x, then the cube root of x (∛x) is n. For example, since 4³ = 64, the cube root of 64 is 4.
