Use the imaginary number 𝑖 to rewrite the expression below as a complex number. Simplify all radicals -√-60

To simplify the expression \(-\sqrt{-60}\) using the imaginary unit \(i\), follow these steps:

1. **Simplify the negative square root**:
   \[
   -\sqrt{-60} = -\sqrt{60} \cdot \sqrt{-1}
   \]
   Since \(\sqrt{-1} = i\), the expression becomes:
   \[
   -\sqrt{60} \cdot i
   \]

2. **Simplify the square root of 60**:
   \[
   \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}
   \]
   So the expression becomes:
   \[
   -2\sqrt{15} \cdot i
   \]

Thus, the simplified form of \(-\sqrt{-60}\) as a complex number is:

\[
-2\sqrt{15}i
\]

Would you like a detailed explanation of any of these steps?

Here are 5 related questions for further practice:
1. Simplify \(\sqrt{-50}\) as a complex number.
2. Simplify \(3\sqrt{-20}\) using the imaginary unit \(i\).
3. Write \(-\sqrt{-75}\) as a complex number.
4. Simplify \(\sqrt{-32}\) as a complex number.
5. Simplify \(-4\sqrt{-45}\) using the imaginary unit \(i\).

**Tip:** When dealing with square roots of negative numbers, always remember to express \(\sqrt{-1}\) as \(i\).

Learn how to simplify the expression -√-60 using imaginary numbers and complex numbers. This problem involves understanding square roots of negative numbers and applying the concept of imaginary unit i. Suitable for high school students.

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