After multiplying by 2, each of the following numbers becomes a perfect square EXCEPT

Options

A. 72
B. 162
C. 392
D. 500

Answer

To solve the problem of identifying which number, when multiplied by 2, does not result in a perfect square, we will analyze each number step by step.

### Step-by-Step Solution:

1. **Examine the first number: 72**
- Multiply by 2:
\[ 72 \times 2 = 144 \]
- Check if 144 is a perfect square:
\[ \sqrt{144} = 12 \quad (\text{since } 12 \times 12 = 144) \]
- Conclusion: 72 multiplied by 2 gives a perfect square.

2. **Examine the second number: 162**
- Multiply by 2:
\[ 162 \times 2 = 324 \]
- Check if 324 is a perfect square:
\[ \sqrt{324} = 18 \quad (\text{since } 18 \times 18 = 324) \]
- Conclusion: 162 multiplied by 2 gives a perfect square.

3. **Examine the third number: 392**
- Multiply by 2:
\[ 392 \times 2 = 784 \]
- Check if 784 is a perfect square:
\[ \sqrt{784} = 28 \quad (\text{since } 28 \times 28 = 784) \]
- Conclusion: 392 multiplied by 2 gives a perfect square.

4. **Examine the fourth number: 500**
- Multiply by 2:
\[ 500 \times 2 = 1000 \]
- Check if 1000 is a perfect square:
\[ \sqrt{1000} = \sqrt{100 \times 10} = 10\sqrt{10} \]
- Since \(10\sqrt{10}\) is not an integer, 1000 is not a perfect square.
- Conclusion: 500 multiplied by 2 does not give a perfect square.

### Final Answer:
The number that does not become a perfect square when multiplied by 2 is **500**.

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