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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.

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โˆ™ 2017-11-22 12:54:00
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Q: If you add a rational and irrational number what is the sum?
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The sum of a rational number and an irrational number and an irrational number is what?

The sum of the three can be rational or irrational.


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The sum of a rational and irrational number must be an irrational number.


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The value of the sum depends on the values of the rational number and the irrational number.


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Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.


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