https://file.aiquickdraw.com/mathbot/file/1728425982858mfwh7era.jpg

The expression you're being asked to simplify is:

\[
\left( \sqrt{-16} \right) \left( \sqrt{-25} \right)
\]

Here’s how to approach it:

1. **Simplify each square root**:
   - \( \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i \) (where \(i\) is the imaginary unit, because \(\sqrt{-1} = i\)).
   - \( \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i \).

2. **Multiply the simplified results**:
   \[
   (4i) \cdot (5i) = 20i^2
   \]

3. **Simplify further using the fact that \(i^2 = -1\)**:
   \[
   20i^2 = 20 \cdot (-1) = -20
   \]

So, the simplified answer is **-20**.

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to deepen understanding:
1. What is the general rule for simplifying square roots of negative numbers?
2. Why is \(i^2\) defined as \(-1\) in complex numbers?
3. How would you multiply other complex numbers like \( (3 + 2i) \) and \( (4 - i) \)?
4. What happens if you have square roots with mixed real and imaginary components, like \( \sqrt{16} \cdot \sqrt{-25} \)?
5. How do you graph complex numbers on the complex plane?

**Tip**: Always handle imaginary numbers carefully, making sure to simplify \(i^2\) when multiplying them!

Multiply (√(-16)) (√(-25)) and simplify your answer.

Learn how to multiply and simplify the imaginary numbers √(-16) and √(-25). This problem explores key concepts in complex numbers and imaginary units, including the use of i² = -1 to simplify results. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation