Question
Write in terms of \( i \). Simplify your answer as much as possible. \( \sqrt{-7} \)
Ask by Ball Reese. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\sqrt{-7} = i\sqrt{7}
\]
Solution
To express \(\sqrt{-7}\) in terms of the imaginary unit \(i\), where \(i = \sqrt{-1}\), follow these steps:
\[
\sqrt{-7} = \sqrt{7} \times \sqrt{-1} = \sqrt{7} \times i = i\sqrt{7}
\]
**Final Answer:**
\[
\sqrt{-7} = i\,\sqrt{7}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To express \( \sqrt{-7} \) in terms of \( i \), we start by recalling that \( i \) is the imaginary unit defined as \( i = \sqrt{-1} \). Thus, we can rewrite \( \sqrt{-7} \) as follows: \[ \sqrt{-7} = \sqrt{7} \cdot \sqrt{-1} = \sqrt{7} \cdot i \] So, the simplified form of \( \sqrt{-7} \) in terms of \( i \) is: \[ \sqrt{-7} = i\sqrt{7} \]
