`{:("Column A" , " ","ColumnB"),(15^2 + 17^2 + 19^2, ,(15 + 17+19)^(2)):}`

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 need to evaluate the expressions in Column A and Column B and compare their values.

### Step 1: Calculate Column A
Column A is given as:
\[ 15^2 + 17^2 + 19^2 \]

Calculating each term:
- \( 15^2 = 225 \)
- \( 17^2 = 289 \)
- \( 19^2 = 361 \)

Now, add these values together:
\[ 15^2 + 17^2 + 19^2 = 225 + 289 + 361 \]
Calculating the sum:
\[ 225 + 289 = 514 \]
\[ 514 + 361 = 875 \]

Thus,
\[ \text{Column A} = 875 \]

### Step 2: Calculate Column B
Column B is given as:
\[ (15 + 17 + 19)^2 \]

First, calculate the sum inside the parentheses:
\[ 15 + 17 + 19 = 51 \]

Now, square this sum:
\[ (51)^2 = 2601 \]

Thus,
\[ \text{Column B} = 2601 \]

### Step 3: Compare Column A and Column B
Now we compare the values obtained:
- Column A = 875
- Column B = 2601

Since \( 2601 > 875 \), we conclude that Column B is greater than Column A.

### Final Conclusion
The value of Column B is larger than the value of Column A.

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