It is rational and, therefore, real.
No it is rational ( all integers are rational)
4/5 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
The square root of four is a real number because it is a non-negative number that can be expressed on the number line. It is also a rational number because it can be expressed as the fraction 2/1. In fact, it is both a real number and a rational number, as all rational numbers are also real numbers.
No because 4/3 is a rational number
Yes, it is.
3/4 is classified as a rational number.
Integer, rational and irrational numner, real number
Yes - any integers, including negative integers, are rational numbers.
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
The given four numbers are all rational numbers
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
-1,0,or 1 the negative square root of four is negative two and the square root of four is two