https://file.aiquickdraw.com/mathbot/file/1728445205160x3i7a5au.jpg

The expression you uploaded is asking to simplify \(\sqrt{-24}\).

Here’s how to simplify it:

1. Recognize that the square root of a negative number involves an imaginary number. Specifically, \(\sqrt{-1} = i\), where \(i\) is the imaginary unit.
2. Now, express the square root of \(-24\) as:
   \[
   \sqrt{-24} = \sqrt{-1 \times 24} = \sqrt{-1} \times \sqrt{24} = i \times \sqrt{24}.
   \]
3. Next, simplify \(\sqrt{24}\):
   \[
   \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}.
   \]
4. Therefore, \(\sqrt{-24} = i \times 2\sqrt{6} = 2i\sqrt{6}\).

So, the simplified form of \(\sqrt{-24}\) is:
\[
2i\sqrt{6}.
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you handle square roots of other negative numbers?
2. What is the significance of the imaginary unit \(i\) in complex numbers?
3. Can square roots of negative numbers be used in real-life applications?
4. How do you simplify radicals like \(\sqrt{48}\) or \(\sqrt{72}\)?
5. How do we multiply or divide expressions involving imaginary numbers?

**Tip:** When simplifying square roots, always check if the number under the radical can be factored into a perfect square, which can be extracted from the radical for easier simplification.

This guide explains how to simplify √-24, covering concepts like imaginary numbers and radical properties. Learn to express negative square roots using the imaginary unit i and simplify radical expressions.

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