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 $\sqrt{-1}$.