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)

1 answer

Let's evaluate the sums in both columns.

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

Column B: \[ 3 - \sqrt{3} + 25 \]

First, simplify \(3 - \sqrt{3} + 25\): \[ 3 + 25 = 28 \] So, we have: \[ 28 - \sqrt{3} \]

Now, we evaluate whether the sums are rational.

  1. Column A: The sum \(34.5\) is a rational number because it can be expressed as \(\frac{69}{2}\).

  2. Column B: The term \(\sqrt{3}\) is an irrational number. Therefore, \(28 - \sqrt{3}\) is also irrational.

Now, we can compare the two columns:

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

Based on the evaluations:

  • 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)

Thus, the correct statement is:

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