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The expression you've provided is the square root of -16, which involves a negative number under the square root. In real numbers, the square root of a negative number is undefined, but in the system of complex numbers, it is represented using the imaginary unit \( i \), where \( i^2 = -1 \).

To solve \( \sqrt{-16} \):

1. First, we express it as:
   \[
   \sqrt{-16} = \sqrt{-1 \times 16}
   \]
2. Then, break it down:
   \[
   \sqrt{-16} = \sqrt{-1} \times \sqrt{16}
   \]
3. Using \( \sqrt{-1} = i \) and \( \sqrt{16} = 4 \):
   \[
   \sqrt{-16} = 4i
   \]

Thus, the result is:
\[
\sqrt{-16} = 4i
\]

Would you like more details or further explanation?

Here are 5 related questions to deepen your understanding:
1. What is the definition of the imaginary unit \( i \)?
2. How do we compute square roots of other negative numbers?
3. What are complex numbers, and how are they represented?
4. Can we add and multiply complex numbers?
5. How does the complex plane help visualize complex numbers?

**Tip:** Imaginary numbers appear when dealing with square roots of negative numbers, and they form the foundation of complex number theory.

Learn how to calculate the square root of -16 using complex numbers. This solution explores the use of the imaginary unit i, where i² = -1, and provides a step-by-step breakdown of the process. Perfect for students learning about complex numbers in Grades 8-10.

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