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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.
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When an irrational number is divided by a rational number is the quotient rational or irrational?
Irrational.
What is the product of rational and irrational number?
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
When you multiply an irrational number by a rational number will the answer always be irrational rational or both?
It will be irrational.
Is the product of a rational number and irrational number always rational?
No.A rational times an irrational is never rational. It is always irrational.
What is the Next to rational and irrational number?
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
