Let's evaluate the sums in both columns.
Column A: \[ 0.5 + 34 = 34.5 \]
Column B: \[ 3 - \sqrt{3} + 25 \]
First, simplify \(3 - \sqrt{3} + 25\): \[ 3 + 25 = 28 \] So, we have: \[ 28 - \sqrt{3} \]
Now, we evaluate whether the sums are rational.
-
Column A: The sum \(34.5\) is a rational number because it can be expressed as \(\frac{69}{2}\).
-
Column B: The term \(\sqrt{3}\) is an irrational number. Therefore, \(28 - \sqrt{3}\) is also irrational.
Now, we can compare the two columns:
- Column A has a rational sum: \(34.5\)
- Column B has an irrational sum: \(28 - \sqrt{3}\)
Based on the evaluations:
- Statement #1: Only Column A has a rational sum. (True)
- Statement #2: Only Column B has a rational sum. (False)
- Statement #3: Column A and Column B both have rational sums. (False)
Thus, the correct statement is:
1