Let's simplify the given expression [tex]\(\sqrt{-100}\)[/tex].
1. Recognize the square root of a negative number: Normally, the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
2. Separate the negative part: We can rewrite [tex]\(\sqrt{-100}\)[/tex] as [tex]\(\sqrt{100} \cdot \sqrt{-1}\)[/tex].
3. Simplify the square root of the positive number:
[tex]\[
\sqrt{100} = 10
\][/tex]
4. Incorporate the imaginary unit:
[tex]\[
\sqrt{-1} = i
\][/tex]
5. Combine the results:
[tex]\[
\sqrt{-100} = 10i
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{-100}\)[/tex] is [tex]\(10i\)[/tex].
So, [tex]\(\sqrt{-100} = 10 \cdot i\)[/tex].
