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 (sqrt)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.

Which statement is true?

Answer 1

To evaluate the two sums in Column A and Column B, we first perform the calculations.

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

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

Next, we need a common denominator to add \(\frac{1}{2}\) and \(\frac{3}{4}\). The common denominator for \(2\) and \(4\) is \(4\).

Convert \(\frac{1}{2}\) to have a denominator of \(4\):
\[ \frac{1}{2} = \frac{2}{4} \]

Now add the fractions:
\[
\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}
\]
So, the sum in Column A is:
\[
\frac{5}{4} \text{ (which is rational)}
\]

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

Here, \(\sqrt{3}\) is an irrational number, and \(\frac{2}{5}\) is a rational number. The sum of a rational number and an irrational number is always irrational. Therefore, the sum in Column B is:
\[
\sqrt{3} + \frac{2}{5} \text{ (which is irrational)}
\]

Now we can compare the results:
- Column A: \(\frac{5}{4}\) (rational)
- Column B: \(\sqrt{3} + \frac{2}{5}\) (irrational)

Now, we analyze the statements provided:

- **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)

The correct statement is:
**Statement #1 is true.**

Thus, the answer is:
**1**