Simplify `sqrt(-7) xx sqrt(-8)` ?

Answer

To simplify the expression \( \sqrt{-7} \times \sqrt{-8} \), we can follow these steps:

### Step 1: Rewrite the square roots of negative numbers
We start by rewriting the square roots of negative numbers using the imaginary unit \( i \), where \( i = \sqrt{-1} \).

\[ \sqrt{-7} = \sqrt{-1} \times \sqrt{7} = i \sqrt{7} \]
\[ \sqrt{-8} = \sqrt{-1} \times \sqrt{8} = i \sqrt{8} \]

### Step 2: Multiply the two expressions
Now we can multiply the two expressions we obtained:

\[ \sqrt{-7} \times \sqrt{-8} = (i \sqrt{7}) \times (i \sqrt{8}) \]

### Step 3: Apply the multiplication
Using the property of multiplication, we can rearrange the terms:

\[ = i \times i \times \sqrt{7} \times \sqrt{8} \]

### Step 4: Simplify \( i \times i \)
We know that \( i^2 = -1 \), so:

\[ = -1 \times \sqrt{7} \times \sqrt{8} \]

### Step 5: Combine the square roots
Using the property of square roots, we can combine \( \sqrt{7} \) and \( \sqrt{8} \):

\[ = -1 \times \sqrt{7 \times 8} = -1 \times \sqrt{56} \]

### Step 6: Final result
Thus, the simplified expression is:

\[ = -\sqrt{56} \]

### Summary
The final answer is:

\[ -\sqrt{56} \]