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The image shows a Khan Academy exercise asking to "Simplify roots of negative numbers." The specific problem displayed is:

**Express the radical using the imaginary unit \( i \). Simplify your answer as much as possible:**

\[ \sqrt{-36} \]

### Solution:
The square root of a negative number can be expressed using the imaginary unit \( i \), where \( i \) is defined as \( i = \sqrt{-1} \).

Given:
\[ \sqrt{-36} \]

We can express this as:
\[ \sqrt{-36} = \sqrt{36 \times (-1)} = \sqrt{36} \times \sqrt{-1} \]

Since \( \sqrt{36} = 6 \) and \( \sqrt{-1} = i \), the expression simplifies to:
\[ \sqrt{-36} = 6i \]

### Final Answer:
\[ 6i \]

Would you like more details or have any questions? Here are some related questions for further practice:

1. How do you simplify \( \sqrt{-49} \) using the imaginary unit?
2. What is the result of \( \sqrt{-25} \)?
3. How would you simplify \( \sqrt{-64} \)?
4. Explain the steps to simplify \( \sqrt{-81} \) using \( i \).
5. How does the imaginary unit \( i \) help in simplifying roots of negative numbers?

**Tip:** Always remember that \( i^2 = -1 \) when working with imaginary numbers. This identity is fundamental in simplifying expressions involving \( i \).

Express the radical using the imaginary unit, i. Simplify your answer as much as possible: √(-36)

Learn how to simplify the square root of a negative number, √(-36), by expressing it using the imaginary unit i. This problem explores the use of imaginary numbers in mathematics and is suitable for high school students (Grades 9-12).

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