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.
Irrational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
No.A rational times an irrational is never rational. It is always irrational.
It will be irrational.
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).
10.01 is a rational number
1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
Rational
It is a rational number.
is 34.54 and irrational or rational. number
it is a rational number but 4.121314..... is an irrational no
Irrational.
Such a product is always irrational - unless the rational number happens to be zero.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
No number is irrational and rational.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
The sum of a rational and irrational number must be an irrational number.