Squares and cubes from 1 to 30
Understand the Problem
The question is asking for the squares and cubes of the numbers from 1 to 30. This requires computation for each number in that range to identify their squares (number raised to the power of 2) and cubes (number raised to the power of 3).
Answer
The squares and cubes of numbers from 1 to 30 are displayed in the table above.
Answer for screen readers
Here are the squares and cubes of the numbers from 1 to 30:
| Number | Square ($n^2$) | Cube ($n^3$) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | 1331 |
| 12 | 144 | 1728 |
| 13 | 169 | 2197 |
| 14 | 196 | 2744 |
| 15 | 225 | 3375 |
| 16 | 256 | 4096 |
| 17 | 289 | 4913 |
| 18 | 324 | 5832 |
| 19 | 361 | 6859 |
| 20 | 400 | 8000 |
| 21 | 441 | 9261 |
| 22 | 484 | 10648 |
| 23 | 529 | 12167 |
| 24 | 576 | 13824 |
| 25 | 625 | 15625 |
| 26 | 676 | 17576 |
| 27 | 729 | 19683 |
| 28 | 784 | 21952 |
| 29 | 841 | 24389 |
| 30 | 900 | 27000 |
Steps to Solve
-
Identify the range of numbers We need to compute the squares and cubes for each integer from 1 to 30.
-
Calculate the squares For a number $n$, the square is calculated as $n^2$. We will compute this for each integer from 1 to 30. Example for the first few numbers:
- For $n = 1$: $1^2 = 1$
- For $n = 2$: $2^2 = 4$
- For $n = 3$: $3^2 = 9$
- Continue until $n = 30$.
- Calculate the cubes For a number $n$, the cube is calculated as $n^3$. We will compute this for the same integers from 1 to 30. Example for the first few numbers:
- For $n = 1$: $1^3 = 1$
- For $n = 2$: $2^3 = 8$
- For $n = 3$: $3^3 = 27$
- Continue until $n = 30$.
- Present the results Compile the results into a list or table format displaying each number, its square, and its cube.
Here are the squares and cubes of the numbers from 1 to 30:
| Number | Square ($n^2$) | Cube ($n^3$) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | 1331 |
| 12 | 144 | 1728 |
| 13 | 169 | 2197 |
| 14 | 196 | 2744 |
| 15 | 225 | 3375 |
| 16 | 256 | 4096 |
| 17 | 289 | 4913 |
| 18 | 324 | 5832 |
| 19 | 361 | 6859 |
| 20 | 400 | 8000 |
| 21 | 441 | 9261 |
| 22 | 484 | 10648 |
| 23 | 529 | 12167 |
| 24 | 576 | 13824 |
| 25 | 625 | 15625 |
| 26 | 676 | 17576 |
| 27 | 729 | 19683 |
| 28 | 784 | 21952 |
| 29 | 841 | 24389 |
| 30 | 900 | 27000 |
More Information
The square of a number represents the area of a square with a side length equal to that number, while the cube of a number represents the volume of a cube with side length equal to that number. This concept is useful in various fields, including geometry and algebra.
Tips
- Confusing squares and cubes: Remember that squaring is raising to the power of 2 and cubing is raising to the power of 3.
- Miscalculating: Double-check calculations especially for larger numbers.
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