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Why is the sum of an rational number and irrational number an irrational number?
Wiki User
∙ 14y ago
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Wiki User
∙ 14y ago
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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.
What is the sum of an rational number and irrational number?
An irrational number.
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.
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.
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
