Answer :
To solve the problem of finding an expression equivalent to [tex]\(\sqrt{-121}\)[/tex], we need to consider that we'll be working with imaginary numbers. Here's how you can think about it step-by-step:
1. Understanding Imaginary Numbers:
- The number [tex]\(-121\)[/tex] is negative, so its square root will involve the imaginary unit, denoted as [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
2. Breaking Down the Expression:
- We can express [tex]\(\sqrt{-121}\)[/tex] as [tex]\(\sqrt{121 \times (-1)}\)[/tex].
- This can be separated into two parts using the property of square roots: [tex]\(\sqrt{121} \times \sqrt{-1}\)[/tex].
3. Calculate Each Part:
- [tex]\(\sqrt{121}\)[/tex] is simply 11, because 11 multiplied by itself gives 121.
- [tex]\(\sqrt{-1}\)[/tex] is represented by [tex]\(i\)[/tex].
4. Combining the Parts:
- Putting these results together, we get [tex]\(11 \times i\)[/tex], which can be written as [tex]\(11i\)[/tex].
Thus, the expression that is equivalent to [tex]\(\sqrt{-121}\)[/tex] is [tex]\(11i\)[/tex], which corresponds to choice D from the given options.
1. Understanding Imaginary Numbers:
- The number [tex]\(-121\)[/tex] is negative, so its square root will involve the imaginary unit, denoted as [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
2. Breaking Down the Expression:
- We can express [tex]\(\sqrt{-121}\)[/tex] as [tex]\(\sqrt{121 \times (-1)}\)[/tex].
- This can be separated into two parts using the property of square roots: [tex]\(\sqrt{121} \times \sqrt{-1}\)[/tex].
3. Calculate Each Part:
- [tex]\(\sqrt{121}\)[/tex] is simply 11, because 11 multiplied by itself gives 121.
- [tex]\(\sqrt{-1}\)[/tex] is represented by [tex]\(i\)[/tex].
4. Combining the Parts:
- Putting these results together, we get [tex]\(11 \times i\)[/tex], which can be written as [tex]\(11i\)[/tex].
Thus, the expression that is equivalent to [tex]\(\sqrt{-121}\)[/tex] is [tex]\(11i\)[/tex], which corresponds to choice D from the given options.