(\sqrt(-8))/(\sqrt(-2)\sqrt(-9))  what does B equal

To simplify the expression:

\[
\frac{\sqrt{-8}}{\sqrt{-2} \cdot \sqrt{-9}}
\]

We first use the property of square roots with negative numbers, which involves imaginary numbers (\(i = \sqrt{-1}\)).

1. **Simplify \(\sqrt{-8}\):**
   \[
   \sqrt{-8} = \sqrt{-1} \cdot \sqrt{8} = i \cdot \sqrt{8} = i \cdot 2\sqrt{2}
   \]

2. **Simplify \(\sqrt{-2}\):**
   \[
   \sqrt{-2} = \sqrt{-1} \cdot \sqrt{2} = i \cdot \sqrt{2}
   \]

3. **Simplify \(\sqrt{-9}\):**
   \[
   \sqrt{-9} = \sqrt{-1} \cdot \sqrt{9} = i \cdot 3 = 3i
   \]

Now, substitute these values back into the original expression:

\[
\frac{i \cdot 2\sqrt{2}}{(i \cdot \sqrt{2}) \cdot (3i)}
\]

4. **Simplify the denominator:**
   \[
   (i \cdot \sqrt{2}) \cdot (3i) = 3i^2 \cdot \sqrt{2} = 3(-1) \cdot \sqrt{2} = -3\sqrt{2}
   \]

5. **Simplify the entire expression:**
   \[
   \frac{i \cdot 2\sqrt{2}}{-3\sqrt{2}} = \frac{2i}{-3} = -\frac{2i}{3}
   \]

So, \( B = -\frac{2i}{3} \).

Would you like a more detailed explanation on any step or have further questions?

Here are 5 related questions to explore:

1. How do we handle square roots of negative numbers in general?
2. What is the imaginary unit \(i\) and its significance in mathematics?
3. Can all negative square roots be simplified in this way?
4. How do we multiply complex numbers involving \(i\)?
5. What are some practical applications of complex numbers?

**Tip:** Remember, \(i^2 = -1\) is crucial when simplifying expressions involving complex numbers.

(\sqrt{-8})/(\sqrt{-2}\sqrt{-9}) what does B equal?

Learn how to simplify the expression (\sqrt{-8})/(\sqrt{-2} \cdot \sqrt{-9}) involving square roots of negative numbers and the imaginary unit. This step-by-step solution covers the key concepts of complex numbers, imaginary numbers (i), and their multiplication. Suitable for high school students in Grades 10-12.

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