Simplify the following
`sqrt(-18).sqrt(-2)`

Answer

To simplify the expression \(\sqrt{-18} \cdot \sqrt{-2}\), we can follow these steps:

### Step 1: Rewrite the square roots of negative numbers
We know that \(\sqrt{-a} = i\sqrt{a}\), where \(i\) is the imaginary unit. Thus, we can rewrite the square roots:

\[ \sqrt{-18} = i\sqrt{18} \]
\[ \sqrt{-2} = i\sqrt{2} \]

### Step 2: Substitute the rewritten square roots into the expression
Now we can substitute these back into the original expression:

\[ \sqrt{-18} \cdot \sqrt{-2} = (i\sqrt{18}) \cdot (i\sqrt{2}) \]

### Step 3: Multiply the terms
Now, we can multiply the terms together:

\[ (i\sqrt{18}) \cdot (i\sqrt{2}) = i^2 \cdot \sqrt{18} \cdot \sqrt{2} \]

### Step 4: Simplify \(i^2\)
We know that \(i^2 = -1\), so we can simplify further:

\[ i^2 \cdot \sqrt{18} \cdot \sqrt{2} = -1 \cdot \sqrt{18} \cdot \sqrt{2} \]

### Step 5: Combine the square roots
Using the property of square roots, \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\):

\[ \sqrt{18} \cdot \sqrt{2} = \sqrt{36} = 6 \]

### Step 6: Final simplification
Substituting back, we have:

\[ -1 \cdot 6 = -6 \]

Thus, the final answer is:

\[ \boxed{-6} \]

---