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

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irrational

Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)

Yes

No. The sum of an irrational number and any other [real] number is irrational.

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.

Related questions

The sum of the three can be rational or irrational.

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

Yes. The sum of two irrational numbers can be rational, or irrational.

No. In fact the sum of a rational and an irrational MUST be irrational.

Not necessarily. The sum of two irrational numbers can be rational or irrational.

It is always irrational.

Such a sum is always irrational.

The sum is irrational.

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

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.

An irrational number.

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