Yes.
a number that cant be written on a number line. (ex. √-1) (the check is a square root sign)
The real number system is composed of the counting numbers (1, 2, 3...).
It can be but it need not be. For example, i/2, where i is the imaginary sqrt of -1, is not real.
1/2 is a rational number
1/2, 5, pi, respectively
The set of natural numbers or counting numbers N is a subset of the set of real numbers R. N = {1, 2, 3, ...) R = {..., -2, -1, -0.5, 0, 1, √2, 2, 3, π, ...}
Yes. It is equal to (1 + sqrt5) / 2 = ~1.618 which, though irrational, is a purely real number; i.e. it has no imaginary component.
2 is a real number.
The discriminant. b^2 - 4ac answer > 1; two real roots answer = 1 one real root answer < 1 no real roots
Yes, square of 2 is a real number. Real numbers fall into 2 categories, Rational and Irrational. Square of 2 is an irrational number.
4.6666667 as a mixed number is 4 2/3.
Yes, 1 1/2 + 1 1/2 = 2 2/2 or 3. The reason why are that real numbers and rational numbers are infinite and can add or subtract to make any number on the number line.