Question
is square root of rpi squared irrational or rational
is 9pi irrational or rational
is 9pi irrational or rational
Answers
GPT-4o mini
Let's analyze both parts of your question:
1. **Square root of \( \pi^2 \)**:
\[
\sqrt{\pi^2} = \pi
\]
Since \(\pi\) is a well-known irrational number, the square root of \(\pi^2\) is also irrational.
2. **Value of \( 9\pi \)**:
- Since \(\pi\) is irrational, any non-zero rational number multiplied by \(\pi\) (in this case, 9) remains irrational. Therefore, \(9\pi\) is irrational.
In summary:
- The square root of \(\pi^2\) is irrational.
- \(9\pi\) is also irrational.
1. **Square root of \( \pi^2 \)**:
\[
\sqrt{\pi^2} = \pi
\]
Since \(\pi\) is a well-known irrational number, the square root of \(\pi^2\) is also irrational.
2. **Value of \( 9\pi \)**:
- Since \(\pi\) is irrational, any non-zero rational number multiplied by \(\pi\) (in this case, 9) remains irrational. Therefore, \(9\pi\) is irrational.
In summary:
- The square root of \(\pi^2\) is irrational.
- \(9\pi\) is also irrational.