Pregunta
Write in terms of \( i \), Simplify your answer as much as possible \[ \sqrt{-100} \]
Ask by Klein Hart. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( \sqrt{-100} = 10i \)
Solución
Calculate or simplify the expression \( \sqrt(-100) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-100}\)
- step1: Evaluate the power:
\(\sqrt{100}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{100}\times i\)
- step3: Evaluate the power:
\(10i\)
The simplified form of \( \sqrt{-100} \) is \( 10i \).
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Simplifique esta solución The Deep Dive
To write \( \sqrt{-100} \) in terms of \( i \), we first recognize that the square root of a negative number can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). We can rewrite \( \sqrt{-100} \) as: \[ \sqrt{-100} = \sqrt{100} \cdot \sqrt{-1} = 10i \] So, the simplified form of \( \sqrt{-100} \) is \( 10i \).
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