Question
Rewrite this imaginary number and select your answer from the choices. \( \sqrt{-56} \)
Ask by Wyatt Mejia. in the United States
Mar 05,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{-56} = 2\sqrt{14}i \)
Solution
Calculate or simplify the expression \( \sqrt{-56} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-56}\)
- step1: Evaluate the power:
\(\sqrt{56}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{56}\times i\)
- step3: Evaluate the power:
\(2\sqrt{14}\times i\)
The imaginary number \( \sqrt{-56} \) can be rewritten as \( 2\sqrt{14}i \).
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Simplify this solution The Deep Dive
To rewrite \( \sqrt{-56} \), we can separate the negative part by using the imaginary unit \( i \) (where \( i = \sqrt{-1} \)). This gives us: \[ \sqrt{-56} = \sqrt{-1} \cdot \sqrt{56} = i \cdot \sqrt{56}. \] Next, we simplify \( \sqrt{56} \). Since \( 56 = 4 \times 14 \), we have: \[ \sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \cdot \sqrt{14} = 2\sqrt{14}. \] So, combining everything, we get: \[ \sqrt{-56} = 2\sqrt{14}i. \]
