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Is the sum or difference of a rational number and an irrational number is irrational?
Wiki User
∙ 12y ago
Yes.
Wiki User
∙ 12y 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.
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be 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.
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
The sum of a rational number and an irrational number?
Such a sum is always irrational.
What is the sum or difference of the any two irrational numbers?
The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
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.
Why is the sum of an rational number and irrational number an irrational number?
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.
