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The given problem asks you to express the radical \(\pm \sqrt{-14}\) using the imaginary unit \(i\), and to simplify the result.

Here’s how we approach it:

1. The square root of a negative number introduces the imaginary unit \(i\), where \(i = \sqrt{-1}\).
2. We can factor \(\sqrt{-14}\) as:
   \[
   \sqrt{-14} = \sqrt{-1} \times \sqrt{14} = i\sqrt{14}
   \]
3. Hence, the expression simplifies to:
   \[
   \pm \sqrt{-14} = \pm i\sqrt{14}
   \]

So, the answer is:
\[
\pm i \sqrt{14}
\]

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

Here are five related questions to expand on this topic:
1. How do you simplify expressions with complex numbers involving square roots?
2. What is the significance of the imaginary unit \(i\)?
3. How would you handle higher powers of the imaginary unit \(i\)?
4. Can you add and subtract imaginary numbers? How does that work?
5. What happens when you multiply two imaginary numbers?

**Tip**: When simplifying square roots of negative numbers, always factor out \(\sqrt{-1} = i\) first before continuing with the rest of the expression.

Express the radical using the imaginary unit, i. Express your answer in simplified form: ±√(-14) = ±

Learn how to express radicals involving negative numbers using the imaginary unit, i. This example shows the step-by-step solution to simplify ±√(-14) to ±i√14, suitable for students in Grades 9-12.

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