Question
Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -\sqrt{-56} \)
Ask by Lyons Johnson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-2\sqrt{14}i\)
Solution
Calculate or simplify the expression \( -\sqrt{-56} \).
Calculate the value by following steps:
- step0: Calculate:
\(-\sqrt{-56}\)
- step1: Simplify the root:
\(-2\sqrt{14}\times i\)
The expression \( -\sqrt{-56} \) can be rewritten as a complex number using the imaginary number \( i \) as follows:
\[
-\sqrt{-56} = -2\sqrt{14} \times i
\]
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Simplify this solution Bonus Knowledge
To rewrite the expression \( -\sqrt{-56} \), we first recognize that the negative inside the square root can be expressed using the imaginary unit \( i \). This gives us: \[ -\sqrt{-56} = -\sqrt{56} \cdot i \] Next, we simplify \( \sqrt{56} \). The number 56 can be factored into \( 28 \times 2 \) or \( 4 \times 14 \). The square root of \( 56 \) simplifies as follows: \[ \sqrt{56} = \sqrt{4 \cdot 14} = \sqrt{4} \cdot \sqrt{14} = 2\sqrt{14} \] Substituting this back into our expression, we get: \[ -\sqrt{-56} = -2\sqrt{14} \cdot i \] Thus, the simplified form of the expression as a complex number is: \[ -2\sqrt{14}i \]
