Question
Which irrational number can be added to Pi to get a sum that is rational?
StartFraction 1 Over pi EndFraction
Negative StartFraction 1 Over pi EndFraction
Negative pi
Pi
StartFraction 1 Over pi EndFraction
Negative StartFraction 1 Over pi EndFraction
Negative pi
Pi
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which irrational number can be added to \(\pi\) to result in a rational sum, we need to analyze the effects of adding each of the provided options:
1. **\(\frac{1}{\pi}\)**: This number is also irrational. The sum \(\pi + \frac{1}{\pi}\) would still be irrational.
2. **\(-\frac{1}{\pi}\)**: This number is irrational as well. The sum \(\pi - \frac{1}{\pi}\) remains irrational.
3. **\(-\pi\)**: This is also irrational. The sum \(\pi - \pi\) equals \(0\), which is rational.
4. **\(\pi\)**: Adding \(\pi\) to \(\pi\) gives \(2\pi\), which is still irrational.
Out of these options, the only one that can be added to \(\pi\) to yield a rational number is \(-\pi\).
Therefore, the answer is: **\(-\pi\)**.
1. **\(\frac{1}{\pi}\)**: This number is also irrational. The sum \(\pi + \frac{1}{\pi}\) would still be irrational.
2. **\(-\frac{1}{\pi}\)**: This number is irrational as well. The sum \(\pi - \frac{1}{\pi}\) remains irrational.
3. **\(-\pi\)**: This is also irrational. The sum \(\pi - \pi\) equals \(0\), which is rational.
4. **\(\pi\)**: Adding \(\pi\) to \(\pi\) gives \(2\pi\), which is still irrational.
Out of these options, the only one that can be added to \(\pi\) to yield a rational number is \(-\pi\).
Therefore, the answer is: **\(-\pi\)**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.