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Answered 2017-11-21 18:47:29
Assuming that you mean pi, and not pie, it is not a rational number.
The set of rational numbers is a field and this means that for every non-zero rational number, there exists a multiplicative inverse in the setand also, due to closure, the product of any two rational numbers is a rational number.
Now suppose 7*pi were rational.
7 is rational and so there is its multiplicative inverse, which is (1/7).
(1/7) is also rational so (1/7)*(7*pi) is rational
But by the associative property, this is (1/7*7)*pi = 1*pi = pi.
But it has been proven that pi is irrational. Therefore the supposition must be wrong ie 7*pi is not rational.
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