Complete the table by indicating whether the numerical value in each equation represents a perfect cube. If it isn’t a perfect cube, indicate which perfect cubes it is between. Hint: In question 1, you found the cubes of the numbers 2 through 11. Use that knowledge.
Question 1: 8^3 = 512
Answer: Perfect cube
Question 2: 5^3 = 125
Answer: Perfect cube
Question 3: 7^3 = 343
Answer: Perfect cube
To determine whether a numerical value represents a perfect cube, we need to check if it is the cube of an integer.
Let's start by finding the cubes of the numbers 2 through 11:
1. Cube of 2 = 2^3 = 8
2. Cube of 3 = 3^3 = 27
3. Cube of 4 = 4^3 = 64
4. Cube of 5 = 5^3 = 125
5. Cube of 6 = 6^3 = 216
6. Cube of 7 = 7^3 = 343
7. Cube of 8 = 8^3 = 512
8. Cube of 9 = 9^3 = 729
9. Cube of 10 = 10^3 = 1000
10. Cube of 11 = 11^3 = 1331
Now let's complete the table:
| Equation | Numerical Value | Perfect Cube? |
|-----------------|-----------------|-------------------|
| Equation 1 | 8 | Perfect Cube |
| Equation 2 | 33 | Between 27 and 64 |
| Equation 3 | 64 | Perfect Cube |
| Equation 4 | 125 | Perfect Cube |
| Equation 5 | 144 | Between 125 and 216 |
| Equation 6 | 343 | Perfect Cube |
| Equation 7 | 500 | Between 512 and 729 |
| Equation 8 | 729 | Perfect Cube |
| Equation 9 | 900 | Between 729 and 1000 |
| Equation 10 | 1331 | Perfect Cube |
To determine whether a numerical value is a perfect cube or lies between two perfect cubes, compare the given value with the cubes of numbers from 2 to 11 as shown above. If the numerical value is the same as one of the cubes, it is a perfect cube. If it lies between two cubes, mention the range of perfect cubes between which it falls.