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No. sqrt(2)/pi is not rational.
Any multiple of or addition to or subtraction from PI is an irrational number. PI divided by PI is 1, a rational number. So is PI times 0 = 0
The square of pi is an irrational number.
pi is an irrational number. It is irrational because it cannot be expressed as a ratio of two integers.
In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.