Question
Write in terms of \( i \). Simplify your answer as much as possible. \( \sqrt{-44} \)
Ask by Munoz Ingram. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{-44} = 2\sqrt{11}\,i \)
Solution
To simplify \( \sqrt{-44} \) in terms of \( i \) (where \( i = \sqrt{-1} \)), follow these steps:
1. **Express the Negative Under the Square Root Using \( i \):**
\[
\sqrt{-44} = \sqrt{-1 \times 44} = \sqrt{-1} \times \sqrt{44} = i \times \sqrt{44}
\]
2. **Simplify \( \sqrt{44} \):**
\[
\sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11}
\]
3. **Combine the Results:**
\[
\sqrt{-44} = i \times 2\sqrt{11} = 2\sqrt{11}\,i
\]
**Final Answer:**
\[
\sqrt{-44} = 2\sqrt{11}\,i
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To express \( \sqrt{-44} \) in terms of \( i \), we first recognize that \( \sqrt{-44} = \sqrt{44} \cdot \sqrt{-1} \). Since \( \sqrt{-1} = i \), we can rewrite this as: \[ \sqrt{-44} = \sqrt{44} \cdot i \] Now, we simplify \( \sqrt{44} \). We can factor 44 into \( 4 \times 11 \), so: \[ \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \cdot \sqrt{11} = 2\sqrt{11} \] Putting it all together, we have: \[ \sqrt{-44} = 2\sqrt{11} \cdot i \] Therefore, the simplified expression for \( \sqrt{-44} \) is: \[ 2\sqrt{11}i \]
