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What The product of two rational numbers?
It is a rational number.
What is the sum or difference of the any two irrational numbers?
The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.
Why the sum difference and product of 2 rational numbers rational?
A rational number is one that can be expressed as a/b The sum of two rational numbers is: a/b + c/d =ad/bd + bc/bd =(ad+bc)/bd =e/f which is rational The difference of two rational numbers is: a/b - c/d =ab/bd - bc/bd =(ab-bc)/bd =e/f which is rational The product of two rational numbers is: (a/b)(c/d) =ac/bd =e/f which is rational
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
Rational numbers between -1 and 3?
There are an infinite number of rational numbers between any two rational numbers.
Must the difference between two rational numbers be a rational number?
Yes.
Is the difference of two rational numbers always rational?
Yes. This is the same as asking for one rational number to be subtracted from another; to do this each rational number is made into an equivalent rational number so that the two rational numbers have the same denominator, and then the numerators are subtracted which gives a rational number which may possibly be simplified.
The difference of two rational numbers is always a rational number?
Yes, that's true.
Is it true that The difference of two rational numbers always a rational number?
Yes. The rational numbers are a closed set with respect to subtraction.
How the difference of two rational numbers can be rational and irrational?
There is no number which can be rational and irrational so there is no point in asking "how".
Why is the difference of two rational numbers always a whole number?
The question cannot be answered because it is nonsensical. The difference between two rational numbers is very very rarely a whole number.
Is The difference of two real numbers always an irrational number?
No. 5 and 2 are real numbers. Their difference, 3, is a rational number.
Would the difference of a rational number and a rational number be rational?
The difference of two rational numbers is rational. Let the two rational numbers be a/b and c/d, where a, b, c, and d are integers. Any rational number can be represented this way. Their difference is a/b-c/d = ad/bd-cb/bd = (ad-cb)/bd. Products and differences of integers are always integers. This means that ad-cb is an integer, and so is bd. Thus, (ad-cb)/bd is a rational number (since it is the ratio of two integers). This is equivalent to the difference of the original two rational numbers.
Is the difference between two rational numbers always a rational numbers?
no
Is the difference between two rational numbers be a rational numbers?
Yes.
How do you insert rational numbers between two rational numbers?
Find the arithmetic average of the two rational numbers. It will be a rational number and will be between the two numbers.
Can you add two rational numbers and get a rational number?
Every time. The sum of two rational numbers MUST be a rational number.
