To determine which of the given numbers are the cubes of odd numbers, we need to follow a series of mathematical steps. Let's go through each number one by one and verify whether they can be expressed as cubes of odd integers.
### Checking 64:
1. Find the cube root of 64.
- [tex]\( \sqrt[3]{64} = 4 \)[/tex]
2. Check if 4 is an odd number.
- 4 is an even number.
So, 64 is not the cube of an odd number.
### Checking 8000:
1. Find the cube root of 8000.
- [tex]\( \sqrt[3]{8000} = 20 \)[/tex]
2. Check if 20 is an odd number.
- 20 is an even number.
So, 8000 is not the cube of an odd number.
### Checking 729:
1. Find the cube root of 729.
- [tex]\( \sqrt[3]{729} = 9 \)[/tex]
2. Check if 9 is an odd number.
- 9 is an odd number.
So, 729 is the cube of an odd number.
### Checking 1331:
1. Find the cube root of 1331.
- [tex]\( \sqrt[3]{1331} = 11 \)[/tex]
2. Check if 11 is an odd number.
- 11 is an odd number.
So, 1331 is the cube of an odd number.
### Final Answer:
Among the given numbers, 729 and 1331 are the cubes of odd numbers.
So, the correct answers are:
(c) 729 and (d) 1331
