Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-48)=+-◻

Express in terms of i: First, we need to express ±sqrt(-48) in terms of i, which represents the square root of -1. ±sqrt(-48) = ±sqrt(-1 * 48)Separate square roots: Next, we can separate the square root of -1 from the square root of 48. ±sqrt(-1 * 48) = ±sqrt(-1) * sqrt(48)Replace sqrt(-1) with i: Now, we replace sqrt(-1) with i, since i is defined as the square root of -1. ±sqrt(-1) * sqrt(48) = ±i * sqrt(48)Simplify sqrt(48): We can simplify sqrt(48) by factoring it into sqrt(16 * 3), since 16 is a perfect square. ±i * sqrt(48) = ±i * sqrt(16 * 3)Take square root of 16: Now, we take the square root of 16, which is 4, outside the radical. ±i * sqrt(16 * 3) = ±i * 4 * sqrt(3)Multiply by 4: Finally, we multiply the 4 by the ±i to get the simplified form. ±i * 4 * sqrt(3) = ±4i * sqrt(3)

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Q. Express the radical using the imaginary unit,

i

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Express your answer in simplified form.

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\pm \sqrt{-48}= \pm \square

Express in terms of i: First, we need to express $\pm\sqrt{-48}$ in terms of $i$ , which represents the square root of $-1$ . $\pm\sqrt{-48} = \pm\sqrt{-1 \times 48}$
Separate square roots: Next, we can separate the square root of $-1$ from the square root of $48$ . $\pm\sqrt{-1 \times 48} = \pm\sqrt{-1} \times \sqrt{48}$
Replace $\sqrt{-1}$ with $i$ : Now, we replace $\sqrt{-1}$ with $i$ , since $i$ is defined as the square root of $-1$ . $\pm\sqrt{-1} \times \sqrt{48} = \pm i \times \sqrt{48}$
Simplify $\sqrt{48}$ : We can simplify $\sqrt{48}$ by factoring it into $\sqrt{16 \times 3}$ , since $16$ is a perfect square. $\newline$ $\pm i \times \sqrt{48} = \pm i \times \sqrt{16 \times 3}$
Take square root of $16$ : Now, we take the square root of $16$ , which is $4$ , outside the radical. $\pm i \cdot \sqrt{16 \cdot 3} = \pm i \cdot 4 \cdot \sqrt{3}$
Multiply by $4$ : Finally, we multiply the $4$ by the $\pm i$ to get the simplified form. $\newline$ $\pm i \times 4 \times \sqrt{3} = \pm 4i \times \sqrt{3}$