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Is the sum of two irrational numbers also an irrational number?
Wiki User
∙ 13y ago
Not necessarily.
3+sqrt(2) and 3-sqrt(2) are both Irrational Numbers. Their sum is 6 - a rational.
Wiki User
∙ 13y ago
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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.
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.
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
Can you add two irrational numbers to get an irrational number?
Yes.An example:1 + 2^(0.5) is an irrational number,1 -(2^(0.5)) is also a irrational number.(1 + 2^(0.5)) + (1- 2^(0.5)) = 22 is a rational number.Therefore the sum of two irrational numbers can equal a rational number.But this is not the question. Can you add two irrational numbers to get another irrational number. Yes. Almost all additions of two irrational numbers result in another irrational number. For instance pi (3.141...) and e (2.718...) are both irrational, and so is their sum. In some sense you have to work quite hard to make the sum not irrational (i.e. rational) because the two decimal expansions have to conspire together either to cancel out or to give a repeating decimal.Actually, pi+e may or may not be irrational. This hasn't been proved either way. See: http://en.wikipedia.org/wiki/Irrational_number (under "Open Questions")Yes. For example, pi + (-pi) = 0.any number that is a non-terminating decimal is called an irrational number.
Is the sum of two irrational numbers irrational?
not always. nothing can be generalized about the sum of two irrational number. counter example. x=(sqrt(2) + 1), y=(1 - sqrt20) then x + y = 1, rational.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
The sum of rational numbers and an irrational number?
It is always an irrational number.
If you add two irrational numbers do you get an irrational number?
Not necessarily. The sum of two irrational numbers can be rational or irrational.
What will be the sum of a rational number and an irrational number?
It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
What is the sum of two irrational numbers?
It may be a rational or an irrational number.
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 2 irrational add to an irrational number?
Yes. The sum of two irrational numbers can be rational, or irrational.
What is an irrational plus two rational numbers?
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
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.
Can the sum of two irrational numbers be a rational number?
Yes
The sum of a rational number and an irrational number?
Such a sum is always irrational.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
