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Answer :
To solve the problem, let's focus on evaluating the expression under the square root: [tex]\(\sqrt{12-32}\)[/tex].
1. Calculate the Expression Inside the Square Root:
- Subtract 32 from 12:
[tex]\[
12 - 32 = -20
\][/tex]
2. Evaluate the Square Root:
- The expression under the square root is [tex]\(-20\)[/tex], which is a negative number.
- In real numbers, the square root of a negative number is not defined because no real number squared gives a negative result.
3. Complex Numbers:
- If we consider complex numbers, the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\)[/tex].
Since the square root involves a complex number, a real number remainder does not exist from this mathematical operation. Therefore, none of the options provided (A, B, C, D) are applicable as the problem involves a complex number situation.
The key takeaway is that the expression has no real remainder due to the presence of a negative number under the square root.
1. Calculate the Expression Inside the Square Root:
- Subtract 32 from 12:
[tex]\[
12 - 32 = -20
\][/tex]
2. Evaluate the Square Root:
- The expression under the square root is [tex]\(-20\)[/tex], which is a negative number.
- In real numbers, the square root of a negative number is not defined because no real number squared gives a negative result.
3. Complex Numbers:
- If we consider complex numbers, the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\)[/tex].
Since the square root involves a complex number, a real number remainder does not exist from this mathematical operation. Therefore, none of the options provided (A, B, C, D) are applicable as the problem involves a complex number situation.
The key takeaway is that the expression has no real remainder due to the presence of a negative number under the square root.
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