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{:("Column A"," ","Column B"),(sq...

`{:("Column A"," ","Column B"),(sqrt(12.5)+sqrt(12.5),,sqrt(25)):}`

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

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to compare the values in Column A and Column B. ### Step-by-Step Solution: **Step 1: Evaluate Column A** - Column A is given as \( \sqrt{12.5} + \sqrt{12.5} \). - This can be simplified as \( 2 \cdot \sqrt{12.5} \). **Step 2: Simplify \( \sqrt{12.5} \)** - Rewrite \( 12.5 \) as \( \frac{125}{10} \) or \( \frac{125}{10} = \frac{25 \cdot 5}{10} = \frac{25}{2} \). - Therefore, \( \sqrt{12.5} = \sqrt{\frac{25}{2}} = \frac{\sqrt{25}}{\sqrt{2}} = \frac{5}{\sqrt{2}} \). **Step 3: Substitute back into Column A** - Now substituting back, we have: \[ 2 \cdot \sqrt{12.5} = 2 \cdot \frac{5}{\sqrt{2}} = \frac{10}{\sqrt{2}}. \] - To rationalize the denominator, multiply the numerator and the denominator by \( \sqrt{2} \): \[ \frac{10}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{10\sqrt{2}}{2} = 5\sqrt{2}. \] **Step 4: Evaluate Column B** - Column B is given as \( \sqrt{25} \). - We know that \( \sqrt{25} = 5 \). **Step 5: Compare Column A and Column B** - Now we compare \( 5\sqrt{2} \) (Column A) and \( 5 \) (Column B). - Since \( \sqrt{2} \approx 1.414 \), we find: \[ 5\sqrt{2} \approx 5 \cdot 1.414 \approx 7.07. \] - Clearly, \( 5\sqrt{2} > 5 \). ### Conclusion: - Therefore, Column A is greater than Column B. ### Final Answer: Column A > Column B. ---
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