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 \( i \).

Explore how to simplify the expression √-18 × √-3 using complex numbers and imaginary units. Learn the step-by-step process, including the use of the imaginary unit i and properties of square roots, suitable for high school students (Grades 9-12).

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