https://file.aiquickdraw.com/mathbot/file/1726024205599w23pnw1z.jpg

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!

Learn to simplify expressions involving the multiplication of square roots of negative numbers using imaginary numbers. This example calculates (√(-9)) * (√(-49)) resulting in a simple integer, demonstrating key concepts of complex numbers and their properties.

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