Question

Evaluate the two sums and determine which statement is true. Enter the correct number associated with your response. Column A Column B 0.5+34 3–√+25 Statement #1: Only Column A has a rational sum. Statement #2: Only Column B has a rational sum. Statement #3: Column A and Column B both have rational sums. (1 point)

Answer 1

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.

1. **Column A:**
The sum \(34.5\) is a rational number because it can be expressed as \(\frac{69}{2}\).

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**