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.
No. A rational plus an irrational is always an irrational.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.
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. In fact, a rational plus or minus an irrational will always be irrational.
10+0.01 = 10.01 and it is a rational number
You can also have any numbers like (a + c) and (b - c), where "c" is the irrational part, and "a" and "b" are rational.
rational. if it can be expressed as a fraction, it is rational.
It is irrational.
Yes.
Yes