To determine which choice is equivalent to the expression [tex]\(\sqrt{-64}\)[/tex], let's break down the computation step by step.
1. Recall that the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
2. The expression [tex]\(\sqrt{-64}\)[/tex] can be expressed in terms of [tex]\(i\)[/tex]. Specifically, [tex]\(\sqrt{-64} = \sqrt{64 \cdot (-1)}\)[/tex].
3. We can separate the square root of the product into the product of the square roots:
[tex]\[
\sqrt{-64} = \sqrt{64} \cdot \sqrt{-1}
\][/tex]
4. We know that [tex]\(\sqrt{64} = 8\)[/tex] because 8 multiplied by itself gives 64.
5. We recognize that [tex]\(\sqrt{-1} = i\)[/tex].
6. Combining these results, we get:
[tex]\[
\sqrt{-64} = 8 \cdot i = 8i
\][/tex]
Thus, the correct choice equivalent to the expression [tex]\(\sqrt{-64}\)[/tex] is:
A. [tex]\(8i\)[/tex]
