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# If you add a rational and irrational number what is the sum?

Wiki User

2017-11-22 12:54:00

an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVED
it will always be irrational.

Wiki User

2017-11-22 12:54:00
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