The value of `(11111)^(2)` is

Options

A. `12344321`
B. `121212121`
C. `123454321`
D. `11344311`

Answer

To find the value of \( (11111)^2 \), we can use the pattern for squaring numbers that consist of repeated digits of 1.

### Step-by-Step Solution:

1. **Identify the Number**: We have the number \( 11111 \).

2. **Count the Digits**: The number \( 11111 \) has 5 digits.

3. **Create the Pattern**: When squaring a number made of \( n \) digits of 1, the result can be represented as a pattern:
- The first half of the result will count up from 1 to \( n \).
- The second half will count down from \( n-1 \) to 1.

4. **Construct the Result**:
- For \( n = 5 \):
- The first half will be: \( 1, 2, 3, 4, 5 \)
- The second half will be: \( 4, 3, 2, 1 \)
- Combining these gives us: \( 123454321 \)

5. **Final Answer**: Therefore, \( (11111)^2 = 123454321 \).