The square root of `((sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)))` is

Options

A. `sqrt(3)+sqrt(2)`
B. `sqrt(3)-sqrt(2)`
C. `sqrt(2)+sqrt(3)`
D. `sqrt(2)-sqrt(3)`

Answer

To solve the question, we need to find the square root of the expression \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\).

### Step-by-step Solution:

1. **Identify the Expression**: We start with the expression:
\[ \sqrt{\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}} \]

2. **Rationalize the Denominator**: To simplify the expression, we will rationalize the denominator. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{3} + \sqrt{2}\):
\[ \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \cdot \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{(\sqrt{3} + \sqrt{2})^2}{(\sqrt{3})^2 - (\sqrt{2})^2} \]

3. **Calculate the Denominator**: The denominator simplifies as follows:
\[ (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1 \]

4. **Calculate the Numerator**: Now we calculate the numerator:
\[ (\sqrt{3} + \sqrt{2})^2 = (\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2 = 3 + 2\sqrt{6} + 2 = 5 + 2\sqrt{6} \]

5. **Combine the Results**: Now we can combine the results:
\[ \frac{(\sqrt{3} + \sqrt{2})^2}{1} = 5 + 2\sqrt{6} \]

6. **Take the Square Root**: Finally, we need to take the square root of the result:
\[ \sqrt{5 + 2\sqrt{6}} \]

7. **Final Result**: The square root of the expression is:
\[ \sqrt{5 + 2\sqrt{6}} \]

### Conclusion:
Thus, the final answer is:
\[ \sqrt{5 + 2\sqrt{6}} \]