Let < x > denote the greatest integer less than or equal to x. For example : `<5.5> = 5` and `<3> = 3`. Now, which column below is larger?
`{:("Column A",xge0,"Column B),(sqrt(x), ,x):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to compare the two columns given:

- Column A: \( \sqrt{x} \)
- Column B: \( x \)

We will evaluate these expressions for different values of \( x \) in the domain \( x \geq 0 \).

### Step-by-Step Solution:

1. **Evaluate for \( x = 0 \)**:
- Column A: \( \sqrt{0} = 0 \)
- Column B: \( 0 \)
- Conclusion: Column A = Column B

2. **Evaluate for \( x = 1 \)**:
- Column A: \( \sqrt{1} = 1 \)
- Column B: \( 1 \)
- Conclusion: Column A = Column B

3. **Evaluate for \( x = 2 \)**:
- Column A: \( \sqrt{2} \approx 1.414 \)
- Column B: \( 2 \)
- Conclusion: Column A < Column B

4. **Evaluate for \( x = 4 \)**:
- Column A: \( \sqrt{4} = 2 \)
- Column B: \( 4 \)
- Conclusion: Column A < Column B

5. **Evaluate for \( x = 9 \)**:
- Column A: \( \sqrt{9} = 3 \)
- Column B: \( 9 \)
- Conclusion: Column A < Column B

6. **General Observation**:
- For \( 0 \leq x < 1 \): \( \sqrt{x} \) is greater than \( x \).
- For \( x = 1 \): \( \sqrt{x} = x \).
- For \( x > 1 \): \( \sqrt{x} < x \).

### Final Conclusion:
From the evaluations, we can conclude that:
- For \( x = 0 \) and \( x = 1 \), both columns are equal.
- For \( x > 1 \), Column B is larger than Column A.
- Therefore, there is not enough information to definitively say which column is larger for all \( x \geq 0 \).

The correct answer is **D: There is not enough information to decide**.