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If x is a rational number and y is a rational number than is x plus y rational?
Wiki User
∙ 7y ago
If both numbers are rational then x plus y is a rational number
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∙ 7y ago
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Show that the sum of rational no with an irrational no is always irrational?
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.
If you add a rational and irrational number what is the sum?
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.
What numbers will produce a rational number when multiplied?
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.
Explain why the sum of a rational number and an irrational number is an irrational number?
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)
If x is rational and y is rational then xy is rational?
Yes, the product of two rational numbers is always a rational number.
If x is a rational number and y is an irrational number what can you say about x plus y?
It is irrational.
Why is the smallest rational number?
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.
If x is a rational number and y is an irrational number then can you say about x plus y?
please rephrase or grammar-check your question.
Show that the sum of rational no with an irrational no is always irrational?
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.
Is there any number x such that x² is an irrational number and x's is a rational number?
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.
What irrational number can be added to pi to get a sum that is rational?
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
What is meant by additive identity in rational numbers?
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
If you add a rational and irrational number what is the sum?
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.
What numbers will produce a rational number when multiplied?
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.
X2 plus 11x plus 6 rational zeros?
x^2 + 11x + 6 has no rational zeros.
What does seven is more than a number mean?
The number plus sevenIf the "number" is X, then seven more than X is X+7
What is a quotient of the rational expression x plus 2 over x plus 8?
That one, there!
