Pregunta
Write in terms of \( i \). Simplify your answer as much as possible. \[ \sqrt{-31} \]
Ask by Guerrero Bates. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\[
\sqrt{-31} = i \sqrt{31}
\]
Solución
To express \(\sqrt{-31}\) in terms of the imaginary unit \(i\), follow these steps:
1. **Recognize the Negative Under the Square Root:**
\[
\sqrt{-31} = \sqrt{-1 \times 31}
\]
2. **Use the Definition of \(i\):**
\[
\sqrt{-1} = i
\]
3. **Simplify the Expression:**
\[
\sqrt{-31} = i \sqrt{31}
\]
So, the simplified form is:
\[
\sqrt{-31} = i \sqrt{31}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To express \( \sqrt{-31} \) in terms of \( i \), we can use the property that \( i \) is defined as \( \sqrt{-1} \). Therefore, we can rewrite \( \sqrt{-31} \) as follows: \[ \sqrt{-31} = \sqrt{31} \cdot \sqrt{-1} = \sqrt{31} \cdot i \] Thus, the simplified form is: \[ \sqrt{-31} = i\sqrt{31} \]
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