The expression given is the square root of $-24$, which involves a negative number under the square root. The square root of a negative number introduces imaginary numbers.

The square root of $-24$ can be expressed as:

$\sqrt{-24} = \sqrt{24} \cdot \sqrt{-1} = \sqrt{24} \cdot i$

Where $i$ is the imaginary unit, defined as $i = \sqrt{-1}$.

Now, simplifying $\sqrt{24}$: $\sqrt{24} = \sqrt{4 \cdot 6} = 2\sqrt{6}$

Thus, the final expression for the square root of $-24$ is:

$\sqrt{-24} = 2\sqrt{6}i$

So, the square root is $2\sqrt{6}i$.

Would you like further clarification or details on this? Here are some related questions you might find useful:

1. What are imaginary numbers, and how are they used in complex number theory?
2. Can negative numbers under square roots have real solutions?
3. How do you simplify square roots of non-perfect squares like $\sqrt{24}$?
4. What is the significance of the imaginary unit $i$ in mathematics?
5. How do square roots behave differently with positive and negative radicands?

Tip: When dealing with negative square roots, always look for an opportunity to use imaginary numbers $i$, as real square roots don't exist for negative numbers.