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

Options

A. 196
B. 441
C. 625
D. 529

Answer

To determine which of the following numbers is the square of an even number, we will analyze the options given:

1. **Identify the options**: The options provided are:
- Option 1: 1, 9, 6
- Option 2: 4, 4, 1
- Option 3: 6, 2, 5
- Option 4: 5, 9

2. **Understand even numbers**: Even numbers are integers that can be divided by 2 without leaving a remainder. Examples of even numbers include 0, 2, 4, 6, 8, 10, etc.

3. **Calculate squares of even numbers**: Let's calculate the squares of the first few even numbers:
- \(2^2 = 4\)
- \(4^2 = 16\)
- \(6^2 = 36\)
- \(8^2 = 64\)
- \(10^2 = 100\)

4. **Identify the unit digits of these squares**: The unit digits of the squares we calculated are:
- Square of 2: 4 (unit digit is 4)
- Square of 4: 16 (unit digit is 6)
- Square of 6: 36 (unit digit is 6)
- Square of 8: 64 (unit digit is 4)
- Square of 10: 100 (unit digit is 0)

From this, we can see that the unit digits of the squares of even numbers can be 0, 4, or 6.

5. **Check the options against the unit digits**:
- **Option 1: 1, 9, 6** - The unit digit is 6 (which is a square of an even number).
- **Option 2: 4, 4, 1** - The unit digit is 4 (which is a square of an even number).
- **Option 3: 6, 2, 5** - The unit digit is 5 (not a square of an even number).
- **Option 4: 5, 9** - The unit digit is 9 (not a square of an even number).

6. **Conclusion**: From the analysis, both Option 1 (6) and Option 2 (4) contain numbers that are squares of even numbers. However, since the question asks for which of the following is a square of an even number, we can conclude that both options are valid.

**Final Answer**: Option 1 (6) and Option 2 (4) are squares of even numbers.