The greater between `sqrt(17)-sqrt(12)` and `sqrt(11)-sqrt(6)` is

Options

A. `sqrt(17)-sqrt(12)`
B. `sqrt(11)-sqrt(6)`
C. Both are equal
D. Cannot compare

Answer

To find the greater value between \( \sqrt{17} - \sqrt{12} \) and \( \sqrt{11} - \sqrt{6} \), we will calculate each expression step by step.

### Step 1: Calculate \( \sqrt{17} \)
Using a calculator or estimation:
\[ \sqrt{17} \approx 4.123 \]

### Step 2: Calculate \( \sqrt{12} \)
Using a calculator or estimation:
\[ \sqrt{12} \approx 3.464 \]

### Step 3: Calculate \( \sqrt{17} - \sqrt{12} \)
Now, we subtract the two values:
\[ \sqrt{17} - \sqrt{12} \approx 4.123 - 3.464 = 0.659 \]

### Step 4: Calculate \( \sqrt{11} \)
Using a calculator or estimation:
\[ \sqrt{11} \approx 3.317 \]

### Step 5: Calculate \( \sqrt{6} \)
Using a calculator or estimation:
\[ \sqrt{6} \approx 2.449 \]

### Step 6: Calculate \( \sqrt{11} - \sqrt{6} \)
Now, we subtract the two values:
\[ \sqrt{11} - \sqrt{6} \approx 3.317 - 2.449 = 0.868 \]

### Step 7: Compare the two results
Now we have:
- \( \sqrt{17} - \sqrt{12} \approx 0.659 \)
- \( \sqrt{11} - \sqrt{6} \approx 0.868 \)

Since \( 0.868 > 0.659 \), we conclude that:
\[ \sqrt{11} - \sqrt{6} \text{ is greater.} \]

### Final Answer:
The greater value is \( \sqrt{11} - \sqrt{6} \).

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