https://file.aiquickdraw.com/mathbot/file/1726744067859911dsd1l.jpg

The expression shown in the image is \( \sqrt{-36} \).

Since the square root of a negative number is not defined in the set of real numbers, we must consider complex numbers. In the realm of complex numbers, the square root of a negative number involves the imaginary unit \( i \), where \( i = \sqrt{-1} \).

Thus:

\[
\sqrt{-36} = \sqrt{36} \times \sqrt{-1} = 6i
\]

So, the answer is \( 6i \), where \( i \) is the imaginary unit.

Would you like further details on this, or do you have any questions?

Here are five related questions to further explore this topic:
1. What is the square root of other negative numbers like \( \sqrt{-25} \)?
2. Can the square root of any negative number be simplified similarly?
3. What is the definition of the imaginary unit \( i \)?
4. How do we perform operations (addition, multiplication, etc.) with imaginary numbers?
5. Can real and imaginary numbers be combined in other ways to form complex numbers?

**Tip**: The square of the imaginary unit \( i \) is \( i^2 = -1 \), which is fundamental in calculations involving complex numbers.

Learn how to find the square root of negative numbers like √-36 using complex numbers and the imaginary unit i. This problem demonstrates key concepts such as the definition of i and the properties of square roots in complex numbers, suitable for Grades 9-12.

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