To simplify the square root of [tex]\( \sqrt{-121} \)[/tex], we need to recognize that we are dealing with the square root of a negative number. When dealing with square roots of negative numbers, we use the imaginary unit [tex]\( i \)[/tex], where [tex]\( i \)[/tex] is defined as [tex]\( \sqrt{-1} \)[/tex].
Here are the steps to simplify [tex]\( \sqrt{-121} \)[/tex]:
1. Recognize the imaginary unit: [tex]\( \sqrt{-121} \)[/tex] involves taking the square root of a negative number, which introduces the imaginary unit [tex]\( i \)[/tex].
2. Extract the positive part: First, take the absolute value of the negative number to simplify. The absolute value of [tex]\(-121\)[/tex] is [tex]\(121\)[/tex].
3. Find the square root of the positive part: Determine the square root of [tex]\(121\)[/tex]. We know that [tex]\( \sqrt{121} = 11 \)[/tex].
4. Combine with the imaginary unit: Since we are taking the square root of a negative number, we multiply the result by the imaginary unit [tex]\( i \)[/tex]. Therefore, [tex]\( \sqrt{-121} = 11i \)[/tex].
After completing these steps, we arrive at the simplified form of [tex]\( \sqrt{-121} \)[/tex].
Thus, the correct answer is [tex]\( 11i \)[/tex].
So, the correct option is:
b [tex]\( 11 i \)[/tex]
