Full solution

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{-15}= \pm \square

Recognize square root of negative number: First, we recognize that the square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ . We can rewrite the square root of $-15$ as the square root of $-1$ times the square root of $15$ . $\newline$ $\pm\sqrt{-15} = \pm\sqrt{-1 \times 15}$
Replace $\sqrt{-1}$ with $i$ : Next, we know that $\sqrt{-1}$ is the definition of the imaginary unit $i$ . So we can replace $\sqrt{-1}$ with $i$ . $\newline$ $\pm\sqrt{-1 \times 15} = \pm i \times \sqrt{15}$
Check if radical can be simplified: Now, we have the expression in terms of the imaginary unit $i$ . However, we need to check if the radical $\sqrt{15}$ can be simplified further. Since $15$ is not a perfect square and does not have any perfect square factors other than $1$ , the radical is already in its simplest form. $\newline$ $\pm i \times \sqrt{15} = \pm i \times \sqrt{15}$
Write expression in simplified form: Finally, we write the expression in its simplified form with the $\pm$ sign indicating both the positive and negative possibilities. $\pm i \sqrt{15} = \pm i\sqrt{15}$