Which of the following is the value of `(sqrt(11)-sqrt(7)) (sqrt(11) + sqrt( 7))`?

Options

A. `-4`
B. `4`
C. `sqrt(11)`
D. `sqrt(7)`

Answer

To solve the expression \((\sqrt{11} - \sqrt{7})(\sqrt{11} + \sqrt{7})\), we can use the difference of squares identity, which states that:

\[ (a - b)(a + b) = a^2 - b^2 \]

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Here, let \(a = \sqrt{11}\) and \(b = \sqrt{7}\).

2. **Apply the difference of squares formula**:
- According to the formula, we have:
\[ (\sqrt{11} - \sqrt{7})(\sqrt{11} + \sqrt{7}) = (\sqrt{11})^2 - (\sqrt{7})^2 \]

3. **Calculate \((\sqrt{11})^2\) and \((\sqrt{7})^2\)**:
- \((\sqrt{11})^2 = 11\)
- \((\sqrt{7})^2 = 7\)

4. **Subtract the results**:
- Now, substitute back into the equation:
\[ 11 - 7 = 4 \]

5. **Final result**:
- Therefore, the value of \((\sqrt{11} - \sqrt{7})(\sqrt{11} + \sqrt{7})\) is \(4\).

### Conclusion:
The answer is \(4\).