The given expression is $\sqrt{-8}$.

Since we are dealing with the square root of a negative number, the solution involves imaginary numbers. The imaginary unit $i$ is defined as $i = \sqrt{-1}$.

Now, we can express $\sqrt{-8}$ as:

$\sqrt{-8} = \sqrt{-1 \times 8} = \sqrt{-1} \times \sqrt{8} = i \times \sqrt{8}$

Next, simplify $\sqrt{8}$. Since $8 = 4 \times 2$, we can write:

$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Thus, the original expression becomes:

$\sqrt{-8} = 2i\sqrt{2}$

So, the final answer is:

$\boxed{2i\sqrt{2}}$

Would you like any further details or clarifications on this?

Here are 5 related questions:

1. How do you simplify $\sqrt{-9}$?
2. What is the general formula for the square root of a negative number?
3. Can you express $\sqrt{-16}$ in terms of $i$?
4. How do you handle complex numbers in algebraic expressions?
5. What is the value of $i^2$?

Tip: Imaginary numbers are essential when dealing with square roots of negative numbers.