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)
The simplified values of both columns indicate that Statement # is true.

Answer 1

Let's evaluate each sum in Column A and Column B to determine their rationality.

**Column A:**
\[
0.5 + 34 = 34.5
\]

34.5 is a rational number.

**Column B:**
\[
3 - \sqrt{3} + 25
\]
First, simplify \(3 - \sqrt{3} + 25\):
\[
= (3 + 25) - \sqrt{3} = 28 - \sqrt{3}
\]

The term \(\sqrt{3}\) is an irrational number. Therefore, \(28 - \sqrt{3}\) is also irrational since subtracting an irrational number from a rational number yields an irrational number.

Now, summarizing the findings:
- Column A: 34.5 (rational)
- Column B: 28 - \(\sqrt{3}\) (irrational)

Based on this analysis, the true statement is:

**Statement #1: Only Column A has a rational sum.**

So the answer is: **1**.