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Explain why the sum of a rational number and an irrational number is an irrational number?
Wiki User
∙ 11y ago
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)
Wiki User
∙ 11y ago
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Is it true that sum of a rational number and irrational number is irrational?
Yes
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
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.
Why an irrational number plus an irrational number equal a rational?
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.
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.
Which number can be added to a rational number to explain that the sum of rational number and an irrational number is irrational?
Any, and every, irrational number will do.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
May the sum of a rational and an irrational number only be a rational number?
No. In fact the sum of a rational and an irrational MUST be irrational.
What is the sum of a rational number and irrational number?
The value of the sum depends on the values of the rational number and the irrational number.
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
What does The sum of a rational number and irrational number equal?
The sum is irrational.
The sum of a rational number and an irrational number?
Such a sum is always irrational.
What is the sum of an rational number and irrational number?
An irrational number.
What is The sum of a ration and an irrational number?
The sum of the three can be rational or irrational.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Is it true that sum of a rational number and irrational number is irrational?
Yes
