Yes. In fact, a rational plus or minus an irrational will always be irrational.
No. A rational plus an irrational is always an irrational.
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.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
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.
Yes
Yes, always.
An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.
Yes. In fact, a rational plus or minus an irrational will always be irrational.
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
No. The sum of an irrational number and any other [real] number is irrational.
No. A rational plus an irrational is always an irrational.
10+0.01 = 10.01 and it is a rational number
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.
Well, darling, when you add two irrational numbers together, they can sometimes magically cancel each other out in such a way that the sum ends up being a rational number. It's like mixing oil and water and somehow getting a delicious vinaigrette. Math can be a wild ride, honey.
It is irrational.
The sum is a rational number.