To simplify $\sqrt{-48}$, we can express it in terms of $i$, the imaginary unit ($i = \sqrt{-1}$).

1. First, rewrite $\sqrt{-48}$ as $\sqrt{48} \times \sqrt{-1}$.
2. $\sqrt{-1} = i$, so this becomes $\sqrt{48} \times i$.
3. Now, simplify $\sqrt{48}$. We know that $48 = 16 \times 3$, so: $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}.$
4. Therefore, $\sqrt{-48} = 4\sqrt{3} \times i$, or $4i\sqrt{3}$.

So, the simplified expression is:

$\sqrt{-48} = 4i\sqrt{3}.$

Let me know if you'd like further clarification or have any additional questions!

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Here are some related questions to explore:

1. How do you simplify square roots of negative numbers in general?
2. What are other examples of square roots of negative numbers, and how do they simplify?
3. What is the geometric interpretation of the imaginary unit $i$?
4. How does the square root of a negative number relate to complex numbers?
5. What is the difference between real and complex square roots?

Tip: When simplifying square roots of negative numbers, always remember to factor out $\sqrt{-1} = i$ and treat it separately from the real number square root.