Question
Write in terms of \( i \). Simplify your answer as much as possible. \[ \sqrt{-80} \]
Ask by Bowers Mcdonald. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{-80} = 4\sqrt{5}i \)
Solution
Calculate or simplify the expression \( \sqrt(-80) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-80}\)
- step1: Evaluate the power:
\(\sqrt{80}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{80}\times i\)
- step3: Evaluate the power:
\(4\sqrt{5}\times i\)
The simplified form of \( \sqrt{-80} \) in terms of \( i \) is \( 4\sqrt{5}i \).
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Simplify this solution Mind Expander
To simplify \( \sqrt{-80} \), we can first express it using the imaginary unit \( i \), since \( i = \sqrt{-1} \). Start by breaking down the square root: \[ \sqrt{-80} = \sqrt{80} \cdot \sqrt{-1} = \sqrt{80} \cdot i \] Next, simplify \( \sqrt{80} \): \[ \sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] Now substituting back: \[ \sqrt{-80} = 4\sqrt{5} \cdot i \] Thus, the simplified form of \( \sqrt{-80} \) is: \[ 4\sqrt{5}i \]
