Let's simplify the expression [tex]\(\sqrt{-36}\)[/tex].
1. Notice that [tex]\(-36\)[/tex] is a negative number inside the square root, which involves dealing with imaginary numbers.
2. Recall that the square root of a negative number can be written in terms of the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
To simplify [tex]\(\sqrt{-36}\)[/tex]:
1. Break down [tex]\(\sqrt{-36}\)[/tex] into [tex]\(\sqrt{-1 \times 36}\)[/tex].
2. Using the property [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we can write:
[tex]\[
\sqrt{-36} = \sqrt{-1 \times 36} = \sqrt{-1} \times \sqrt{36}
\][/tex]
3. We know [tex]\(\sqrt{-1} = i\)[/tex] and [tex]\(\sqrt{36} = 6\)[/tex].
4. Therefore:
[tex]\[
\sqrt{-36} = i \times 6 = 6i
\][/tex]
So, the simplified form of [tex]\(\sqrt{-36}\)[/tex] is:
[tex]\[
6i
\][/tex]
The correct answer is:
C. [tex]\(6i\)[/tex]
