Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-72)=+-◻

Expressing sqrt(-72): First, we need to express ±sqrt(-72) as the product of the square root of a positive number and the square root of -1. ±sqrt(-72) = ±sqrt(-1 * 72)Recognizing sqrt(-1): Next, we recognize that sqrt(-1) is the definition of the imaginary unit i. ±sqrt(-1 * 72) = ±sqrt(-1) * sqrt(72) = ±i * sqrt(72)Simplifying sqrt(72): Now, we simplify sqrt(72). Since 72 is 36 times 2 and 36 is a perfect square, we can simplify further. sqrt(72) = sqrt(36 * 2) = sqrt(36) * sqrt(2) = 6 * sqrt(2)Multiplying by the imaginary unit i: Finally, we multiply the simplified square root by the imaginary unit i. ±i * sqrt(72) = ±i * 6 * sqrt(2) = ±6i * sqrt(2)

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

+-sqrt(-72)=+-◻

Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-72}= \pm \square$

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Q. Express the radical using the imaginary unit,

i

\newline

Express your answer in simplified form.

\newline

\pm \sqrt{-72}= \pm \square

Expressing $\sqrt{-72}$ : First, we need to express $\pm\sqrt{-72}$ as the product of the square root of a positive number and the square root of $-1$ . $\newline$ $\pm\sqrt{-72} = \pm\sqrt{-1 \times 72}$
Recognizing $\sqrt{-1}$ : Next, we recognize that $\sqrt{-1}$ is the definition of the imaginary unit $i$ .
$\pm\sqrt{-1 \cdot 72} = \pm\sqrt{-1} \cdot \sqrt{72} = \pm i \cdot \sqrt{72}$
Simplifying $\sqrt{72}$ : Now, we simplify $\sqrt{72}$ . Since $72$ is $36$ times $2$ and $36$ is a perfect square, we can simplify further. $\newline$ $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6 \times \sqrt{2}$
Multiplying by the imaginary unit i: Finally, we multiply the simplified square root by the imaginary unit i. $\newline$ $\pm i \cdot \sqrt{72} = \pm i \cdot 6 \cdot \sqrt{2} = \pm 6i \cdot \sqrt{2}$