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 $i$.