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Sum of an irrational number and a rational number is always irrational. Take for example 1/2 + 
. Clearly, 1/2 is rational and its decimal expansion is equal to 0.5, while 
is irrational and has a non-repeating, non-terminating decimal expansion. When you add the two, you are obviously going to get a non-repeating, non-terminating decimal expansion, hence the sum is irrational.