Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-35)=+-

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(-35) by factoring out -1 from under the radical to separate the real and imaginary parts. ±sqrt(-35) = ±sqrt(-1 * 35)Replacing sqrt(-1) with i: Next, we know that sqrt(-1) is the definition of the imaginary unit i. So we can replace sqrt(-1) with i and continue simplifying the expression. ±sqrt(-1 * 35) = ±i * sqrt(35)Simplifying the expression: Since 35 is a product of 5 and 7, and neither 5 nor 7 has a square root that is an integer, we cannot simplify the radical any further. Therefore, the expression is already in its simplest form. ±i * sqrt(35) = ±i√35

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

+-sqrt(-35)=+-

Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-35}= \pm$

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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{-35}= \pm

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 $\pm\sqrt{-35}$ by factoring out $-1$ from under the radical to separate the real and imaginary parts. $\newline$ $\pm\sqrt{-35} = \pm\sqrt{-1 \cdot 35}$
Replacing $\sqrt{-1}$ with $i$ : Next, we know that $\sqrt{-1}$ is the definition of the imaginary unit $i$ . So we can replace $\sqrt{-1}$ with $i$ and continue simplifying the expression. $\newline$ $\pm\sqrt{-1 \times 35} = \pm i \times \sqrt{35}$
Simplifying the expression: Since $35$ is a product of $5$ and $7$ , and neither $5$ nor $7$ has a square root that is an integer, we cannot simplify the radical any further. Therefore, the expression is already in its simplest form. $\newline$ $\pm i \cdot \sqrt{35} = \pm i\sqrt{35}$