Evaluate the two summons to determine which statement is true enter the correct number associated with the response column a 0.5 + 3/4 column b radical 3 + 2/5 statement one only column a has a rational sum statement 2 only column b has a rational Stone statement 3 column a and b both have rational sums the simplified values of both columns indicate that statement number blank is

Answer 1

To evaluate the sums in columns A and B, we'll simplify each expression and determine whether the sum is rational or irrational.

Column A: \(0.5 + \frac{3}{4}\)

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

2. Find a common denominator to add \(\frac{1}{2}\) and \(\frac{3}{4}\):

   • The common denominator is \(4\).
   • Convert \(\frac{1}{2}\) to have a denominator of \(4\): \[ \frac{1}{2} = \frac{2}{4} \]

3. Now add: \[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] The sum is \( \frac{5}{4} \), which is rational.

Column B: \(\sqrt{3} + \frac{2}{5}\)

1. \(\sqrt{3}\) is an irrational number.

2. \(\frac{2}{5}\) is a rational number.

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

Now let's evaluate the statements:

1. Statement 1: "Only Column A has a rational sum." (True)
2. Statement 2: "Only Column B has a rational sum." (False)
3. Statement 3: "Both Column A and B have rational sums." (False)

Based on this analysis, the correct number associated with the true statement is 1.