https://file.aiquickdraw.com/mathbot/file/1727405741287b2k2vfuc.jpg

The expression in the image is \( \sqrt{-24} \). 

This is an example of a square root of a negative number, which involves complex numbers. The square root of a negative number can be rewritten using the imaginary unit \(i\), where \(i = \sqrt{-1}\).

We can express this as:
\[
\sqrt{-24} = \sqrt{-1 \times 24} = \sqrt{-1} \times \sqrt{24} = i \times \sqrt{24}
\]
Now, simplifying \( \sqrt{24} \):
\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\]
Thus, the final simplified form is:
\[
\sqrt{-24} = 2i\sqrt{6}
\]

Would you like further details or have any other questions?

Here are five related questions:
1. How do you simplify square roots of negative numbers generally?
2. What is the significance of the imaginary unit \(i\) in complex numbers?
3. How do you simplify radicals like \( \sqrt{24} \)?
4. What are some applications of complex numbers in physics or engineering?
5. How do you add or subtract complex numbers?

**Tip:** When simplifying square roots of negative numbers, always factor out \( \sqrt{-1} \) as \(i\) first.

What is the simplified form of the square root of -24?

Learn how to simplify the square root of -24 using complex numbers. This problem covers key mathematical concepts, including imaginary numbers and simplifying radicals. Suitable for students in Grades 9-12.

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