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Rational numbers - can be expressed as a fraction, and can be terminating and repeating decimals. Irrational Numbers - can't be turned into fractions, and are non-repeating and non-terminating. (like pi)
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Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Identify of rational and irrational numbers?
A rational number is a number that can be expressed as a ratio of two integers in the form A/B where B>0. An irrational number is a real number that is not rational.
Why is the product of two rational number irrational?
The question is nonsense because the product of two rational numbers is never irrational.
Can you add two irrational numbers to get a rational number?
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.
Can rational numbers be irrational numbers?
No, they are two separate groups of numbers. A number is either rational or irrational, never both.
