`{:("Column A", " ","Column B"),(sqrt(3) + sqrt(5)," ",sqrt(8)):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we will compare the values in Column A and Column B step by step.

### Step 1: Calculate the value of Column A
Column A is given as \( \sqrt{3} + \sqrt{5} \).

1. Find the approximate values of \( \sqrt{3} \) and \( \sqrt{5} \):
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt{5} \approx 2.236 \)

2. Add these values together:
\[ \sqrt{3} + \sqrt{5} \approx 1.732 + 2.236 = 3.968 \]

### Step 2: Calculate the value of Column B
Column B is given as \( \sqrt{8} \).

1. Simplify \( \sqrt{8} \):
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \sqrt{2} \]

2. Find the approximate value of \( \sqrt{2} \):
- \( \sqrt{2} \approx 1.414 \)

3. Multiply to find \( \sqrt{8} \):
\[ 2 \sqrt{2} \approx 2 \times 1.414 = 2.828 \]

### Step 3: Compare the values of Column A and Column B
Now we have:
- Column A: \( \sqrt{3} + \sqrt{5} \approx 3.968 \)
- Column B: \( \sqrt{8} \approx 2.828 \)

### Conclusion
Since \( 3.968 > 2.828 \), we conclude that:
- Column A is greater than Column B.

Thus, the answer is that Column A is larger.