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.

Answer 1

To evaluate Column A and Column B, we will calculate each sum step-by-step.

**Column A:**
\[
0.5 + \frac{3}{4}
\]

Convert \(0.5\) to a fraction:
\[
0.5 = \frac{1}{2}
\]

Now add \(\frac{1}{2}\) and \(\frac{3}{4}\):
To add these fractions, we need a common denominator. The least common denominator of \(2\) and \(4\) is \(4\):
\[
\frac{1}{2} = \frac{2}{4}
\]

Now add:
\[
\frac{2}{4} + \frac{3}{4} = \frac{2+3}{4} = \frac{5}{4}
\]

**Column A Sum:**
\[
\frac{5}{4} \quad \text{(This is a rational number.)}
\]

---

**Column B:**
\[
\sqrt{3} + \frac{2}{5}
\]

Here, \(\sqrt{3}\) is an irrational number, while \(\frac{2}{5}\) is a rational number.

The sum of an irrational number and a rational number is always irrational. Thus:
\[
\sqrt{3} + \frac{2}{5} \quad \text{(This is an irrational number.)}
\]

---

**Conclusion:**

- Column A has a sum of \(\frac{5}{4}\) which is rational.
- Column B has a sum of \(\sqrt{3} + \frac{2}{5}\) which is irrational.

So, the true statement is:

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

Therefore, the answer is **Statement #1.**