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Rewrite this imaginary number using \( i \) and then select your answer from the choices. Make sure the answer is fully simplified. \( \sqrt{-81} \)

Ask by Gibson Barnett. in the United States
Mar 17,2025

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The answer is \( 9i \).

Solución

Calculate or simplify the expression \( \sqrt{-81} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{-81}\) - step1: Evaluate the power: \(\sqrt{81}\times \sqrt{-1}\) - step2: Evaluate the power: \(\sqrt{81}\times i\) - step3: Evaluate the power: \(9i\) The imaginary number \( \sqrt{-81} \) can be rewritten as \( 9i \), where \( i \) is the imaginary unit. Therefore, the answer is \( 9i \).

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To rewrite \( \sqrt{-81} \) using \( i \), we first recognize that \( i \) is the imaginary unit defined as \( i = \sqrt{-1} \). Therefore, we can express \( \sqrt{-81} \) as: \[ \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \] So the fully simplified answer is \( 9i \).

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