What is the sum of StartRoot negative 2 EndRoot and StartRoot negative 18 EndRoot?
4 StartRoot 2 EndRoot
4 StartRoot 2 EndRoot i
5 StartRoot 2 EndRoot
5 StartRoot 2 EndRoot i

The sum of \( \sqrt{-2} \) and \( \sqrt{-18} \) involves imaginary numbers because the square roots of negative numbers are not real. We can express these roots in terms of imaginary units.

### Step-by-step:

1. \( \sqrt{-2} = \sqrt{2} \cdot i \), where \( i \) is the imaginary unit.
2. \( \sqrt{-18} = \sqrt{18} \cdot i = \sqrt{9 \cdot 2} \cdot i = 3\sqrt{2} \cdot i \).

Now, adding \( \sqrt{-2} \) and \( \sqrt{-18} \):

\[
\sqrt{-2} + \sqrt{-18} = \sqrt{2} \cdot i + 3\sqrt{2} \cdot i
\]

This simplifies to:

\[
(\sqrt{2} + 3\sqrt{2}) \cdot i = 4\sqrt{2} \cdot i
\]

Thus, the sum is:

\[
4\sqrt{2} \cdot i
\]

The correct answer is:
\[
\boxed{4\sqrt{2} \cdot i}
\]

Would you like more details or further clarifications?

Here are 5 related questions:
1. How do we simplify square roots of negative numbers?
2. What are imaginary numbers and how do they work?
3. Can we add real and imaginary numbers?
4. What is the imaginary unit \( i \) and why is it important?
5. How do we handle operations with complex numbers?

**Tip:** When simplifying roots of negative numbers, always express them using the imaginary unit \( i \).

What is the sum of StartRoot negative 2 EndRoot and StartRoot negative 18 EndRoot?

Learn how to find the sum of the square roots of negative numbers, such as \( \sqrt{-2} \) and \( \sqrt{-18} \), by expressing them in terms of imaginary numbers. This detailed guide explains key mathematical concepts involving imaginary and complex numbers for students in Grades 9-12.

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