Question
\( \leftarrow \begin{array}{l}\text { Express in terms of } i \\ \sqrt{-343}\end{array} \)
Ask by Bird Frazier. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\sqrt{-343} = 7\sqrt{7}i\)
Solution
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Beyond the Answer
To express \( \sqrt{-343} \) in terms of \( i \), first recognize that \( \sqrt{-1} = i \). Thus, we can rewrite: \[ \sqrt{-343} = \sqrt{343} \cdot \sqrt{-1} = \sqrt{343} \cdot i \] The next step is to simplify \( \sqrt{343} \). Since \( 343 = 7^3 \), we find: \[ \sqrt{343} = \sqrt{7^3} = 7\sqrt{7} \] Putting it all together, we get: \[ \sqrt{-343} = 7\sqrt{7} \cdot i \]
