Write the imaginary number in simplified form: the square root of negative 144

To simplify the square root of a negative number, we use the imaginary unit \(i\), which is defined as:

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

Given the square root of \(-144\), we can rewrite it as:

\[
\sqrt{-144} = \sqrt{144 \cdot (-1)} = \sqrt{144} \cdot \sqrt{-1}
\]

Since \(\sqrt{-1} = i\), the expression simplifies to:

\[
\sqrt{144} \cdot i = 12i
\]

So, the square root of \(-144\) in simplified form is:

\[
\boxed{12i}
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the square root of \(-225\) in simplified form?
2. How do you multiply two imaginary numbers?
3. How do you find the magnitude of a complex number?
4. What is the cube root of a negative number?
5. How do you add and subtract imaginary numbers?

**Tip:** Remember that imaginary numbers are based on the fundamental property that \(i^2 = -1\).

This problem demonstrates how to simplify the square root of negative 144 using the concept of imaginary numbers. It walks through key steps, such as applying the square root of 144 and using the imaginary unit i, resulting in the simplified form 12i. Suitable for students in Grades 9-11.

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