Is the following computation correct? If not give the correct computation: `[sqrt((-2))dotsqrt((-3))]=sqrt((-2)dot(-3))=sqrt(6)`

Explanation

To determine whether the computation \(\sqrt{-2} \cdot \sqrt{-3} = \sqrt{-2 \cdot -3} = \sqrt{6}\) is correct, we need to analyze each step carefully.

### Step-by-Step Solution:

1. **Understanding the Original Expression:**
\[ \sqrt{-2} \cdot \sqrt{-3} \]
Here, both \(-2\) and \(-3\) are negative numbers.

2. **Using the Property of Square Roots:**
The property \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\) holds only when both \(a\) and \(b\) are non-negative. Since both \(-2\) and \(-3\) are negative, we cannot apply this property directly.

3. **Calculating Each Square Root:**
We can express the square roots of negative numbers in terms of imaginary numbers:
\[ \sqrt{-2} = i\sqrt{2} \quad \text{and} \quad \sqrt{-3} = i\sqrt{3} \]

4. **Multiplying the Square Roots:**
Now, we multiply the two results:
\[ \sqrt{-2} \cdot \sqrt{-3} = (i\sqrt{2}) \cdot (i\sqrt{3}) = i^2 \cdot \sqrt{2} \cdot \sqrt{3} \]

5. **Simplifying the Expression:**
Since \(i^2 = -1\), we have:
\[ i^2 \cdot \sqrt{2} \cdot \sqrt{3} = -1 \cdot \sqrt{2} \cdot \sqrt{3} = -\sqrt{6} \]

6. **Conclusion:**
Therefore, the correct computation is:
\[ \sqrt{-2} \cdot \sqrt{-3} = -\sqrt{6} \]

### Final Answer:
The original computation is incorrect. The correct computation is:
\[ \sqrt{-2} \cdot \sqrt{-3} = -\sqrt{6} \]