Which of the following are the cubes of odd numbers?
(i) 125 (ii) 343 (iii) 1728 (iv) 4096 (v) 9261

Answer

To determine which of the given numbers are cubes of odd numbers, we will analyze each number step by step.

### Step 1: Identify the cubes of the given numbers
1. **125**: We can express this as \(5 \times 5 \times 5 = 5^3\).
2. **343**: This can be expressed as \(7 \times 7 \times 7 = 7^3\).
3. **1728**: This can be expressed as \(12 \times 12 \times 12 = 12^3\).
4. **4096**: This can be expressed as \(16 \times 16 \times 16 = 16^3\).
5. **9261**: This can be expressed as \(21 \times 21 \times 21 = 21^3\).

### Step 2: Determine if the base numbers are odd or even
- **125**: The base is 5, which is an odd number.
- **343**: The base is 7, which is an odd number.
- **1728**: The base is 12, which is an even number.
- **4096**: The base is 16, which is an even number.
- **9261**: The base is 21, which is an odd number.

### Step 3: List the cubes of odd numbers
From our analysis:
- **125** (from \(5^3\)) is a cube of an odd number.
- **343** (from \(7^3\)) is a cube of an odd number.
- **1728** (from \(12^3\)) is not a cube of an odd number.
- **4096** (from \(16^3\)) is not a cube of an odd number.
- **9261** (from \(21^3\)) is a cube of an odd number.

### Conclusion
The cubes of odd numbers from the list are:
- **125**
- **343**
- **9261**