Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-24)=+-◻

Express as product of square roots: Express ±sqrt(-24) as the product of square roots and sqrt(-1). ±sqrt(-24) = ±sqrt(-1 * 24)Factor 24 into prime factors: Factor 24 into its prime factors to simplify the square root. 24 = 2^3 * 3 So, ±sqrt(24) = ±sqrt(2^3 * 3)Simplify square root of 24: Simplify the square root of 24 by taking out the square root of 4 (which is a perfect square and a factor of 24). ±sqrt(2^3 * 3) = ±sqrt(2^2 * 2 * 3) = ±2 * sqrt(2 * 3) = ±2 * sqrt(6)Express sqrt(-1) as i: Express ±sqrt(-1) as the imaginary unit i. ±sqrt(-1) = ±iCombine results: Combine the results from Step 3 and Step 4 to express the original expression as a complex number. ±sqrt(-24) = ±i * 2 * sqrt(6) = ±2i * sqrt(6)

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Express the radical using the imaginary unit,
i.
Express your answer in simplified form.

+-sqrt(-24)=+-◻

Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-24}= \pm \square$

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Algebra 2

Introduction to complex numbers

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Q. Express the radical using the imaginary unit,

i

\newline

Express your answer in simplified form.

\newline

\pm \sqrt{-24}= \pm \square

Express as product of square roots: Express $\pm\sqrt{-24}$ as the product of square roots and $\sqrt{-1}$ . $\newline$ $\pm\sqrt{-24} = \pm\sqrt{-1 \cdot 24}$
Factor $24$ into prime factors: Factor $24$ into its prime factors to simplify the square root. $\newline$ $24 = 2^3 \times 3$ $\newline$ So, $\pm\sqrt{24} = \pm\sqrt{2^3 \times 3}$
Simplify square root of $24$ : Simplify the square root of $24$ by taking out the square root of $4$ (which is a perfect square and a factor of $24$ ). $\newline$ $\pm\sqrt{2^3 \times 3} = \pm\sqrt{2^2 \times 2 \times 3}$ $\newline$ = $\pm 2 \times \sqrt{2 \times 3}$ $\newline$ = $\pm 2 \times \sqrt{6}$
Express $\sqrt{-1}$ as $i$ : Express $\pm\sqrt{-1}$ as the imaginary unit $i$ . $\pm\sqrt{-1} = \pm i$
Combine results: Combine the results from Step $3$ and Step $4$ to express the original expression as a complex number. $\newline$ $\pm\sqrt{-24} = \pm i \cdot 2 \cdot \sqrt{6}$ $\newline$ $= \pm 2i \cdot \sqrt{6}$