Question
expression. Use imaginary numbers when 2. \( \sqrt{-16} \) a. \( 16 i \) b. \( 4 i \) c. \( \sqrt{16} i \) d. \( 8 i \) 3. \( \sqrt{-10} \) I. \( \sqrt{10 i} \) m. \( 5 i \) n. \( i \sqrt{ } \) o. -10
Ask by Crawford Murray. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
2. \( \sqrt{-16} = 4i \)
3. \( \sqrt{-10} = i\sqrt{10} \)
Solution
We need to simplify the square roots of negative numbers by writing them in terms of the imaginary unit i (where i² = –1).
2. To simplify √(–16), notice that:
√(–16) = √(16)·√(–1) = 4·i = 4i.
Thus, the correct answer is 4i (option b).
3. To simplify √(–10), note that:
√(–10) = √(10)·√(–1) = √(10)·i = i√10.
Looking at the provided options, the one that corresponds to this result is option n (which represents i√10).
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Simplify this solution Beyond the Answer
The square root of -16 can be simplified using imaginary numbers. We know that \( \sqrt{-1} = i \), so \( \sqrt{-16} \) can be expressed as \( \sqrt{16} \cdot \sqrt{-1} = 4i \). Therefore, the correct answer is b. \( 4 i \). For \( \sqrt{-10} \), the same principle applies. We simplify it as \( \sqrt{10} \cdot \sqrt{-1} = \sqrt{10}i \). This means none of the provided options directly represent the answer. However, since option n. includes an \( i \), it could imply that \( \sqrt{-10} \) is meant to represent \( i \sqrt{10} \), making that the best fit out of the choices given.
