Answer :
To determine which expression is equivalent to [tex]\(18 - \sqrt{-25}\)[/tex], we'll start by analyzing the square root of the negative number involved.
1. Consider the expression [tex]\(\sqrt{-25}\)[/tex]. To handle the negative number inside the square root, we convert it into an imaginary number since the square root of a negative number involves 'i', the imaginary unit, where [tex]\(i^2 = -1\)[/tex].
2. Thus, [tex]\(\sqrt{-25}\)[/tex] can be rewritten using the property of imaginary numbers:
[tex]\[ \sqrt{-25} = \sqrt{25 \cdot (-1)} = \sqrt{25} \cdot \sqrt{-1} = 5i \][/tex]
3. With [tex]\(\sqrt{-25}\)[/tex] now expressed as [tex]\(5i\)[/tex], we can substitute this back into the original expression:
[tex]\[ 18 - \sqrt{-25} = 18 - 5i \][/tex]
4. Therefore, the given expression [tex]\(18 - \sqrt{-25}\)[/tex] simplifies to:
[tex]\[ 18 - 5i \][/tex]
After analyzing and simplifying the expression, we conclude that [tex]\(18 - \sqrt{-25}\)[/tex] is equivalent to:
[tex]\[ \boxed{18 - 5i} \][/tex]
1. Consider the expression [tex]\(\sqrt{-25}\)[/tex]. To handle the negative number inside the square root, we convert it into an imaginary number since the square root of a negative number involves 'i', the imaginary unit, where [tex]\(i^2 = -1\)[/tex].
2. Thus, [tex]\(\sqrt{-25}\)[/tex] can be rewritten using the property of imaginary numbers:
[tex]\[ \sqrt{-25} = \sqrt{25 \cdot (-1)} = \sqrt{25} \cdot \sqrt{-1} = 5i \][/tex]
3. With [tex]\(\sqrt{-25}\)[/tex] now expressed as [tex]\(5i\)[/tex], we can substitute this back into the original expression:
[tex]\[ 18 - \sqrt{-25} = 18 - 5i \][/tex]
4. Therefore, the given expression [tex]\(18 - \sqrt{-25}\)[/tex] simplifies to:
[tex]\[ 18 - 5i \][/tex]
After analyzing and simplifying the expression, we conclude that [tex]\(18 - \sqrt{-25}\)[/tex] is equivalent to:
[tex]\[ \boxed{18 - 5i} \][/tex]
