To solve for [tex]\(\sqrt{-5}\)[/tex] given that [tex]\(x \geq 0\)[/tex] and [tex]\(\sqrt{-x} = i \sqrt{x}\)[/tex]:
1. Identify the value of [tex]\(x\)[/tex]:
Here, we are given [tex]\(x = 5\)[/tex].
2. Substitute [tex]\(x\)[/tex] into the equation:
We need to find [tex]\(\sqrt{-5}\)[/tex].
According to the given condition, [tex]\(\sqrt{-x} = i \sqrt{x}\)[/tex].
3. Apply the formula:
Substitute [tex]\(x = 5\)[/tex] into the formula:
[tex]\[
\sqrt{-5} = i \sqrt{5}
\][/tex]
4. Calculate [tex]\(\sqrt{5}\)[/tex]:
The value of [tex]\(\sqrt{5}\)[/tex] is approximately 2.23606797749979.
5. Multiply by [tex]\(i\)[/tex]:
Thus,
[tex]\[
\sqrt{-5} = i \cdot 2.23606797749979
\][/tex]
6. Result:
Hence, the value of [tex]\(\sqrt{-5}\)[/tex] is:
[tex]\[
2.23606797749979j
\][/tex]
