Answer :
To solve the problem of finding which expression is equivalent to [tex]\(18 - \sqrt{-25}\)[/tex]:
1. Identify the square root of the negative number:
- The number we need to find the square root of is [tex]\(-25\)[/tex].
- The square root of [tex]\(-25\)[/tex] involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i\)[/tex] is defined as [tex]\(\sqrt{-1}\)[/tex].
- Thus, [tex]\(\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i\)[/tex].
2. Substitute the imaginary root back into the expression:
- We need to substitute [tex]\(\sqrt{-25}\)[/tex] with [tex]\(5i\)[/tex] in the original expression [tex]\(18 - \sqrt{-25}\)[/tex].
- So, the expression becomes [tex]\(18 - 5i\)[/tex].
3. Compare this with the given options:
- [tex]\(5i\)[/tex]
- [tex]\(18 - 5i\)[/tex]
- [tex]\(18 + 5i\)[/tex]
- 23
4. Select the equivalent expression:
- Reviewing the given options, it is clear that [tex]\(18 - 5i\)[/tex] directly matches our result from step 2.
Therefore, the expression that is equivalent to [tex]\(18 - \sqrt{-25}\)[/tex] is [tex]\(\boxed{18 - 5i}\)[/tex].
1. Identify the square root of the negative number:
- The number we need to find the square root of is [tex]\(-25\)[/tex].
- The square root of [tex]\(-25\)[/tex] involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i\)[/tex] is defined as [tex]\(\sqrt{-1}\)[/tex].
- Thus, [tex]\(\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i\)[/tex].
2. Substitute the imaginary root back into the expression:
- We need to substitute [tex]\(\sqrt{-25}\)[/tex] with [tex]\(5i\)[/tex] in the original expression [tex]\(18 - \sqrt{-25}\)[/tex].
- So, the expression becomes [tex]\(18 - 5i\)[/tex].
3. Compare this with the given options:
- [tex]\(5i\)[/tex]
- [tex]\(18 - 5i\)[/tex]
- [tex]\(18 + 5i\)[/tex]
- 23
4. Select the equivalent expression:
- Reviewing the given options, it is clear that [tex]\(18 - 5i\)[/tex] directly matches our result from step 2.
Therefore, the expression that is equivalent to [tex]\(18 - \sqrt{-25}\)[/tex] is [tex]\(\boxed{18 - 5i}\)[/tex].
