Question
Rewrite this imaginary number using \( i \) and then select the best choice. Make sure the answer is fully simplified. \[ \sqrt{-2} \]
Ask by Harrington Hardy. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{-2} = \sqrt{2} \times i \)
Solution
Calculate or simplify the expression \( \sqrt{-2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-2}\)
- step1: Evaluate the power:
\(\sqrt{2}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{2}\times i\)
The imaginary number \( \sqrt{-2} \) can be rewritten as \( \sqrt{2} \times i \), where \( i \) is the imaginary unit.
Therefore, the best choice is \( \sqrt{2} \times i \).
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Simplify this solution Extra Insights
The imaginary number \( \sqrt{-2} \) can be rewritten using \( i \) as follows: \[ \sqrt{-2} = \sqrt{2} \cdot i \] This is because \( i \) is defined as \( \sqrt{-1} \), allowing us to separate the negative part from the positive. So, the fully simplified form is \( \sqrt{2} i \).
