Which of the following is the square of an odd number ?

Options

A. 2116
B. 3844
C. 1369
D. 2500

Answer

To determine which of the given options is the square of an odd number, we can follow these steps:

### Step 1: Identify Odd Numbers
First, we need to identify what odd numbers are. Odd numbers are integers that are not divisible by 2. Examples of odd numbers include 1, 3, 5, 7, 9, etc.

### Step 2: Calculate Squares of Odd Numbers
Next, we will calculate the squares of the first few odd numbers:
- The square of 1 is \(1^2 = 1\)
- The square of 3 is \(3^2 = 9\)
- The square of 5 is \(5^2 = 25\)
- The square of 7 is \(7^2 = 49\)
- The square of 9 is \(9^2 = 81\)

From this, we can see that the squares of odd numbers yield results that end in 1 or 9.

### Step 3: Analyze the Options
Now, let's analyze the options provided in the question:
1. Option 1: 2, 1, 6
2. Option 2: 3, 8, 4
3. Option 3: 1, 3, 6
4. Option 4: 2, 5, 0, 0

We will check the unit digits of each option:
- **Option 1**: The unit digits are 2, 1, and 6. The only relevant digit is 1.
- **Option 2**: The unit digits are 3, 8, and 4. None of these are 1, 9, or 5.
- **Option 3**: The unit digits are 1, 3, and 6. The relevant digit is 1.
- **Option 4**: The unit digits are 2, 5, 0, and 0. The relevant digit is 5.

### Step 4: Determine the Correct Option
From our analysis, we see that:
- Option 1 has a unit digit of 1.
- Option 3 has a unit digit of 1.
- Option 4 has a unit digit of 5.

However, we need to find the square of an odd number. The only option that fits the criteria of having a unit digit of 1 or 9 is **Option 3** (1, 3, 6), as it contains the digit 1, which is the square of the odd number 1.

### Conclusion
Thus, the correct answer is **Option 3: 1, 3, 6**.

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