The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
No, never.
Yes. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
No. 3x plus 2x = 5x. 3x multiplied by 2x = 6x²
No, nor is it a real number. The square root of minus 54 is equal to the square root of plus 45, times i.
Yes. In fact, a rational plus or minus an irrational will always be irrational.
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.
No, never.
Yes
Yes, always.
If both numbers are rational then x plus y is a rational number
It does not. A negative number multiplied by a negative number equals a positive number.
Yes, it is.
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.
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.
Yes, the sum is always rational.
That depends what the value of a is.
They add up to 17.02 which is rational number