Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-77)=+-◻

Recognizing the Imaginary Unit: First, we recognize that the square root of a negative number involves the imaginary unit i, where i^2 = -1. We can rewrite the expression ±sqrt(-77) by factoring out -1 from under the radical to separate the imaginary unit from the real number. ±sqrt(-77) = ±sqrt(-1 * 77)Factoring Out -1: Next, we can express the square root of -1 as i, and then take the square root of the remaining positive number, which is 77. ±sqrt(-1 * 77) = ±i * sqrt(77)Expressing the Square Root of -1: Since 77 is not a perfect square, we cannot simplify the square root of 77 any further. Therefore, the expression remains as is. ±i * sqrt(77) = ±i * sqrt(77)

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

+-sqrt(-77)=+-◻

Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-77}= \pm \square$

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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{-77}= \pm \square

Recognizing the Imaginary Unit: First, we recognize that the square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ . We can rewrite the expression $\pm\sqrt{-77}$ by factoring out $-1$ from under the radical to separate the imaginary unit from the real number. $\newline$ $\pm\sqrt{-77} = \pm\sqrt{-1 \times 77}$
Factoring Out $-1$ : Next, we can express the square root of $-1$ as $i$ , and then take the square root of the remaining positive number, which is $77$ . $\newline$ $\pm\sqrt{-1 \times 77} = \pm i \times \sqrt{77}$
Expressing the Square Root of $-1$ : Since $77$ is not a perfect square, we cannot simplify the square root of $77$ any further. Therefore, the expression remains as is. $\newline$ $\pm i \cdot \sqrt{77} = \pm i \cdot \sqrt{77}$