Let's analyze the expression:

$(\sqrt{-9}) \cdot (\sqrt{-49})$

1. The square roots of negative numbers involve imaginary numbers. Specifically: $\sqrt{-9} = 3i \quad \text{(since } \sqrt{9} = 3 \text{ and } \sqrt{-1} = i\text{)}$ $\sqrt{-49} = 7i \quad \text{(since } \sqrt{49} = 7 \text{ and } \sqrt{-1} = i\text{)}$

2. Now multiply these two expressions: $(3i) \cdot (7i) = 21i^2$

3. Since $i^2 = -1$, we get: $21i^2 = 21 \times (-1) = -21$

Thus, the simplified answer is:

$-21$

Would you like more details on any step?

Here are 5 related questions for practice:

1. What is $\sqrt{-16}$?
2. How do you simplify $i^4$?
3. Multiply $\sqrt{-4}$ and $\sqrt{-16}$.
4. Simplify $(5i) \times (6i)$.
5. What is the result of $i^3$?

Tip: Always remember that $i^2 = -1$, which is crucial in simplifying expressions with imaginary numbers!