QuestionAugust 25, 2025

Write in terms of i. Simplify your answer as much as possible. -sqrt (-24)

Write in terms of i. Simplify your answer as much as possible. -sqrt (-24)
Write in terms of i. Simplify your answer as much as possible. -sqrt (-24)

Solution
4.0(236 votes)

Answer

\(-2\sqrt{6}i\) Explanation 1. Simplify the square root of a negative number Recognize that \(-\sqrt{-24}\) can be rewritten using ( ( \(i\) ) ), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-24} = \sqrt{24} \cdot i\). 2. Simplify \(\sqrt{24}\) Factor 24 as \(4 \times 6\), so \(\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}\). 3. Combine results Substitute back to get \(-\sqrt{-24} = -(2\sqrt{6} \cdot i) = -2\sqrt{6}i\).

Explanation

1. Simplify the square root of a negative number<br /> Recognize that \(-\sqrt{-24}\) can be rewritten using ( \(i\) ), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-24} = \sqrt{24} \cdot i\).<br /><br />2. Simplify \(\sqrt{24}\)<br /> Factor 24 as \(4 \times 6\), so \(\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}\).<br /><br />3. Combine results<br /> Substitute back to get \(-\sqrt{-24} = -(2\sqrt{6} \cdot i) = -2\sqrt{6}i\).
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