https://file.aiquickdraw.com/mathbot/file/17284452717103oiw5gbi.jpg

The expression in the image is asking to simplify \( \sqrt{-10} \).

This involves a negative number under the square root, which is not a real number. In mathematics, the square root of a negative number introduces imaginary numbers.

To simplify:

\[
\sqrt{-10} = \sqrt{-1} \times \sqrt{10} = i\sqrt{10}
\]

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

Thus, the simplified form is \( i\sqrt{10} \).

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. How do you simplify the square root of other negative numbers?
2. What is the significance of the imaginary unit \( i \) in complex numbers?
3. How do you add or subtract imaginary numbers?
4. How can we represent complex numbers in the polar form?
5. How do complex numbers appear in real-world applications?

**Tip:** Whenever you see a negative number inside a square root, think of using imaginary numbers, since real square roots only apply to non-negative numbers.

Learn how to simplify the square root of a negative number, such as √(-10), using imaginary numbers. This problem involves key concepts in algebra and the introduction of the imaginary unit i, suitable for students in Grades 9-12.

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