The expression involves multiplying square roots of negative numbers, which results in complex numbers. Let's break it down:

$\sqrt{-18} \times \sqrt{-3}$

We can rewrite each square root of a negative number in terms of the imaginary unit $i$ (where $i = \sqrt{-1}$):

$\sqrt{-18} = \sqrt{18} \cdot i \quad \text{and} \quad \sqrt{-3} = \sqrt{3} \cdot i$

Now, multiplying these:

$(\sqrt{18} \cdot i) \times (\sqrt{3} \cdot i) = \sqrt{18} \times \sqrt{3} \times i^2$

Since $i^2 = -1$:

$\sqrt{18} \times \sqrt{3} \times (-1) = -\sqrt{18 \times 3} = -\sqrt{54}$

Now, simplify $\sqrt{54}$:

$\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}$

Thus, the final result is:

$-\sqrt{54} = -3\sqrt{6}$

Final Answer:

$\sqrt{-18} \times \sqrt{-3} = -3\sqrt{6}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you simplify complex numbers involving square roots?
2. What is the imaginary unit $i$ and how is it used in math?
3. How do you simplify the square root of a product like $\sqrt{54}$?
4. What are the properties of imaginary numbers in multiplication?
5. How do you simplify expressions involving $i^2$?

Tip: When dealing with square roots of negative numbers, always remember to express them in terms of the imaginary unit $i$.