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Q: If x is a rational number and y is a rational number than is x plus y rational?

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It is irrational.

There can be no such thing. Given any rational number, x, the number x/2 is also rational and is smaller than x. This process can be continued for ever.

please rephrase or grammar-check your question.

no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.

Suppose x is a rational number and y is an irrational number.Let x + y = z, and assume that z is a rational number.The set of rational number is a group.This implies that since x is rational, -x is rational [invertibility].Then, since z and -x are rational, z - x must be rational [closure].But z - x = y which implies that y is rational.That contradicts the fact that y is an irrational number. The contradiction implies that the assumption [that z is rational] is incorrect.Thus, the sum of a rational number x and an irrational number y cannot be rational.

The additive identity for rational numbers is 0. It is the only rational number such that, for any rational number x, x + 0 = 0 + x = x

Minus pi. Or minus pi plus any rational number. Here is how you can figure this out (call your unknown number "x", and let "r" stand for any rational number):x + pi = r To solve for "x", simply subtract pi from both sides. That gives you: x = r - pi

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 PROVEDit will always be irrational.

Any number will be a rational number when multiplied.0 multiplied by any real number is rational and so it will produce a rational number when multiplied.If x is any non-zero number (rational or not), then since it is non-zero, 1/x is defined and x*(1/x) = 1 which is rational. So any non-zero number will produce a rational number when multiplied.Thus any number will produce a rational number when multiplied.

The number plus sevenIf the "number" is X, then seven more than X is X+7

x^2 + 11x + 6 has no rational zeros.

That one, there!

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