The square root of \(-8\) involves the use of imaginary numbers since you can't take the square root of a negative number in the set of real numbers.

\[
\sqrt{-8} = \sqrt{8 \cdot (-1)} = \sqrt{8} \cdot \sqrt{-1}
\]

The square root of \(-1\) is represented by the imaginary unit \(i\). So:

\[
\sqrt{-8} = \sqrt{8} \cdot i = 2\sqrt{2} \cdot i
\]

Thus, the square root of \(-8\) is:

\[
\sqrt{-8} = 2\sqrt{2}i
\]

Would you like further details or clarification on imaginary numbers?

Here are five related questions for further exploration:
1. What is the square root of \(-16\)?
2. How do imaginary numbers combine with real numbers?
3. What is the magnitude of a complex number like \(2\sqrt{2}i\)?
4. How do we represent complex numbers graphically?
5. How do you multiply two complex numbers?

**Tip**: When dealing with negative square roots, always remember to include the imaginary unit \(i\), which is defined as \(\sqrt{-1}\).

Discover how to find the square root of -8 by using imaginary numbers. This solution covers key mathematical concepts such as complex numbers and imaginary units, with a step-by-step guide to the formula √(-n) = √n * i. Suitable for students in Grades 10-12.

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