Question
Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -10-\sqrt{-68} \)
Ask by Robbins Sullivan. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( -10 - 2\sqrt{17}i \)
Solution
Calculate or simplify the expression \( -10-\sqrt{-68} \).
Calculate the value by following steps:
- step0: Calculate:
\(-10-\sqrt{-68}\)
- step1: Simplify the root:
\(-10-2\sqrt{17}\times i\)
The expression \( -10-\sqrt{-68} \) can be rewritten as a complex number using the imaginary number \( i \) as follows:
\[
-10-\sqrt{-68} = -10-2\sqrt{17}i
\]
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Simplify this solution Beyond the Answer
To rewrite the expression \( -10 - \sqrt{-68} \) as a complex number, we first note that \( \sqrt{-68} \) can be expressed using the imaginary unit \( i \). We start by simplifying \( \sqrt{-68} \): \[ \sqrt{-68} = \sqrt{68} \cdot \sqrt{-1} = \sqrt{68} i \] Next, we simplify \( \sqrt{68} \): \[ \sqrt{68} = \sqrt{4 \times 17} = \sqrt{4} \cdot \sqrt{17} = 2\sqrt{17} \] Now, substituting this back into our expression gives us: \[ -10 - \sqrt{-68} = -10 - 2\sqrt{17} i \] So the final expression as a complex number is: \[ -10 - 2\sqrt{17} i \]
