To simplify [tex]\(\sqrt{-50}\)[/tex], follow these steps:
1. Recognize that the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex]. Specifically, [tex]\(\sqrt{-1}\)[/tex] is represented as [tex]\(i\)[/tex].
2. Rewrite the expression [tex]\(\sqrt{-50}\)[/tex] as [tex]\(\sqrt{-1 \times 50}\)[/tex].
3. Using the property of square roots, we can separate this into two square roots: [tex]\(\sqrt{-1} \times \sqrt{50}\)[/tex].
4. Recall that [tex]\(\sqrt{-1} = i\)[/tex]. So, the expression now becomes [tex]\(i \times \sqrt{50}\)[/tex].
5. Next, break down [tex]\(\sqrt{50}\)[/tex]:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}
\][/tex]
6. Since [tex]\(\sqrt{25} = 5\)[/tex], substitute this value in:
[tex]\[
\sqrt{50} = 5 \times \sqrt{2}
\][/tex]
7. Substitute [tex]\(\sqrt{50}\)[/tex] back into the expression:
[tex]\[
i \times \sqrt{50} = i \times 5 \times \sqrt{2} = 5i\sqrt{2}
\][/tex]
So, the simplified form of [tex]\(\sqrt{-50}\)[/tex] is:
[tex]\[
5i\sqrt{2}
\][/tex]
Therefore, the correct choice is:
[tex]\(\boxed{5 i \sqrt{2}}\)[/tex]
