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+3/4 √3+2/5

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

To evaluate the sums in Column A and Column B, we start with each column separately.

**Column A:**
\[
0.5 + \frac{3}{4}
\]
First, we convert \(0.5\) to a fraction:
\[
0.5 = \frac{1}{2}
\]
Now we can add the two fractions:
\[
\frac{1}{2} + \frac{3}{4}
\]
To add these, we need a common denominator. The common denominator between \(2\) and \(4\) is \(4\):
\[
\frac{1}{2} = \frac{2}{4}
\]
Now we can add:
\[
\frac{2}{4} + \frac{3}{4} = \frac{5}{4}
\]
Thus, the sum in Column A is:
\[
\frac{5}{4} \quad (\text{which is rational})
\]

**Column B:**
\[
\sqrt{3} + \frac{2}{5}
\]
Here, \( \sqrt{3} \) is an irrational number. Since the sum of a rational number and an irrational number is always irrational, we know that:
\[
\sqrt{3} + \frac{2}{5} \quad (\text{which is irrational})
\]

Now we compare the sums from both columns:
- Column A: \( \frac{5}{4} \) (rational)
- Column B: \( \sqrt{3} + \frac{2}{5} \) (irrational)

Now we evaluate the statements:
- 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)**

Based on the evaluations, the true statement is:
**Statement #1.**

So the final answer is:
**1**