To simplify the expression $\sqrt{-27}$, we need to deal with the negative sign inside the square root, which involves using imaginary numbers.

Here's the process:

$\sqrt{-27} = \sqrt{-1 \times 27} = \sqrt{-1} \times \sqrt{27}$

Since $\sqrt{-1} = i$, where $i$ is the imaginary unit, the expression becomes:

$\sqrt{-27} = i \times \sqrt{27}$

Now, simplify $\sqrt{27}$:

$\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$

So, the simplified form of $\sqrt{-27}$ is:

$\sqrt{-27} = 3i\sqrt{3}$

Thus, the final simplified expression is:

$\boxed{3i\sqrt{3}}$

Would you like more details or have any questions? Here are 5 related questions for further practice:

1. Simplify $\sqrt{-50}$.
2. Simplify $\sqrt{-72}$.
3. What is the value of $i^2$?
4. Simplify $\sqrt{-8}$.
5. Express $\sqrt{-18}$ in its simplest form.

Tip: When simplifying radicals with negative numbers, always remember to factor out $\sqrt{-1}$ as $i$, the imaginary unit!