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Answer :
To solve the problem of finding the remainder in the synthetic division problem, we need to start by understanding what is being asked. The expression given is [tex]\(\sqrt{46-1}\)[/tex], which simplifies to [tex]\(\sqrt{45}\)[/tex].
To solve this, follow these steps:
1. Calculate the Square Root:
- First, simplify the expression inside the square root: [tex]\(46 - 1 = 45\)[/tex].
- Then, find the square root of 45. While [tex]\(\sqrt{45}\)[/tex] is approximately 6.708 (since it doesn't result in a whole number), we don't need an exact decimal.
2. Consider the Concept of Remainder:
- In mathematics, when we talk about remainder, we're often dealing with integer division. However, since the square root results in a non-integer, the 'remainder' in this context might need another interpretation.
3. Identifying the Closest Integer:
- The key part here is to determine the closest integer part from possible answer choices after considering any division interpretation.
In exercises like these, the focus is often on closeness or rounding given practical interpretations. Given the context, the remainder involves rounding [tex]\(\sqrt{45} \approx 6.708\)[/tex] to its nearest integer.
Thus, the closest integer part from the given choices, assuming a division-like scenario with remainder, is most reasonably interpreted here as:
D. 3
This assumes choosing an integer closest to the result of any division interpretations possible with the question, relevant to synthetic scenarios or other practical interpretations given such wording.
To solve this, follow these steps:
1. Calculate the Square Root:
- First, simplify the expression inside the square root: [tex]\(46 - 1 = 45\)[/tex].
- Then, find the square root of 45. While [tex]\(\sqrt{45}\)[/tex] is approximately 6.708 (since it doesn't result in a whole number), we don't need an exact decimal.
2. Consider the Concept of Remainder:
- In mathematics, when we talk about remainder, we're often dealing with integer division. However, since the square root results in a non-integer, the 'remainder' in this context might need another interpretation.
3. Identifying the Closest Integer:
- The key part here is to determine the closest integer part from possible answer choices after considering any division interpretation.
In exercises like these, the focus is often on closeness or rounding given practical interpretations. Given the context, the remainder involves rounding [tex]\(\sqrt{45} \approx 6.708\)[/tex] to its nearest integer.
Thus, the closest integer part from the given choices, assuming a division-like scenario with remainder, is most reasonably interpreted here as:
D. 3
This assumes choosing an integer closest to the result of any division interpretations possible with the question, relevant to synthetic scenarios or other practical interpretations given such wording.
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