Evaluate the two sums and determine which statement is true. Enter the correct number associated with your response.

Question

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.

Answer 1

Let's evaluate the sums in both columns.

Column A: The expression is \( 0.5 + 34 \).

Calculating this: \[ 0.5 + 34 = 34.5 \]

34.5 is a rational number (it can be expressed as the fraction \( \frac{69}{2} \)).

Column B: The expression is \( 3 - \sqrt{3} + 25 \).

Calculating this: \[ 3 - \sqrt{3} + 25 = 28 - \sqrt{3} \]

Here, \( \sqrt{3} \) is an irrational number. Therefore, \( 28 - \sqrt{3} \) is also irrational since the difference of a rational number and an irrational number is irrational.

Now that we have the sums:

• Column A: \( 34.5 \) (rational)
• Column B: \( 28 - \sqrt{3} \) (irrational)

Now, let's assess 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)

Therefore, the correct number associated with the true statement is 1.