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

+-sqrt(-70)=+-

Express the radical using the imaginary unit, $i$ . Express your answer in simplified form. $\newline$ $\pm \sqrt{-70}= \pm$

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Introduction to complex numbers

Full solution

Q. Express the radical using the imaginary unit,

i

. Express your answer in simplified form.

\newline

\pm \sqrt{-70}= \pm

Recognize and Rewrite Expression: 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 $\pm\sqrt{-70}$ by factoring out $-1$ from under the radical to separate the real and imaginary parts. $\newline$ $\pm\sqrt{-70} = \pm\sqrt{-1 \times 70}$
Replace with Imaginary Unit: 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. $\newline$ $\pm\sqrt{-1 \times 70} = \pm i \times \sqrt{70}$
Simplify Square Root of $70$ : Now, we look to simplify $\sqrt{70}$ . Since $70$ is not a perfect square, we check if it has any square factors. The prime factorization of $70$ is $2 \times 5 \times 7$ , which does not contain any repeated factors, so $\sqrt{70}$ cannot be simplified further. $\newline$ Therefore, the expression remains as $\pm i \times \sqrt{70}$ .

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