For all numbers x[x] denotes the value of `x^3` rounded to the nearest multiple of ten.
`{:("Column A",0 < x < 2,"Column B"),(x^2,,sqrt(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 analyze the expressions in Column A and Column B given the constraint \(0 < x < 2\).

### Step 1: Understand the expressions in both columns
- **Column A**: \(x^2\)
- **Column B**: \(\sqrt{x}\)

### Step 2: Analyze the range of \(x\)
Given that \(0 < x < 2\), we can evaluate the two expressions within this range.

### Step 3: Calculate values for \(x^2\) and \(\sqrt{x}\)
1. **For \(x = 1\)**:
- \(x^2 = 1^2 = 1\)
- \(\sqrt{x} = \sqrt{1} = 1\)
- Both columns are equal.

2. **For \(x = 0.5\)**:
- \(x^2 = (0.5)^2 = 0.25\)
- \(\sqrt{x} = \sqrt{0.5} \approx 0.707\)
- Here, \(x^2 < \sqrt{x}\).

3. **For \(x = 1.5\)**:
- \(x^2 = (1.5)^2 = 2.25\)
- \(\sqrt{x} = \sqrt{1.5} \approx 1.225\)
- Here, \(x^2 > \sqrt{x}\).

### Step 4: Conclusion from the evaluations
- At \(x = 1\), both expressions are equal.
- At \(x = 0.5\), \(x^2\) is less than \(\sqrt{x}\).
- At \(x = 1.5\), \(x^2\) is greater than \(\sqrt{x}\).

### Step 5: Determine the overall relationship
Since the relationship between \(x^2\) and \(\sqrt{x}\) changes depending on the value of \(x\) within the interval \(0 < x < 2\), we cannot definitively say which column is larger for all \(x\) in the given range.

### Final Answer
Thus, the correct option is:
**D: There is not enough information to decide.**