0
What else can I help you with?
Example for sum of a rational number and irrational number?
example for sum of rational numbers is 1/3 + 1/5 Example for sum of irrationals is Pi + e where e is is base of natural log Another is square root of 2 + square root of 3.
Is the set of irrational numbers closed for addition?
No. Sqrt(2) is irrational, as is -sqrt(2). Both belong to the irrationals but their sum, 0, is rational.
What will be the sum of irrational numbers?
There is no answer. If the sum is taken for irrationals positive irrationals only, then the answer is clearly + infinity, since the irrationals increase without limit. But there are negative irrationals so we need to consider the sum of irrationals from - infinity to + infinity. Each irrational has a matching negative irrational and these two sets are exhaustive. So, each can be paired off, and one might think that the sum of an infinite pairs of zeros is zero, right? NO, unfortunately not. The logic fails when the sum is over infinitely many terms as is illustrated below: 1-1+1-1 ... = 1+(-1+1)+(-1+1) ... = 1+0+0 ... = 1 or 1-1+1-1 ... = (1-1)+(1-1)+ ... = 0+0+ ... = 0 Incidentally, the above example was used to "prove" that 1 = 0
Can the sum of two irrational numbers be rational if give an example if not explain why not?
1 + sqrt(2) is irrational 1 - sqrt(2) is irrational. Their sum is 2 = 2/1 which is rational.
Is there a rational number between any two irrational numbers?
Yes. To find it, evaluate both irrationals until the numbers show a difference in one of their later digits. Truncate the irrationals after this digit, sum them, then divide by 2. Job done.
Is the sum of two irrational number is always irrational?
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.
The sum of two irrational is always irrational?
No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.
Is the sum of irrational roots irrational?
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
The sum of a rational number and an irrational number?
Such a sum is always irrational.
Why is the sum of two irrational numbers not always irrational?
Because the irrational parts may cancel out.For example, 1 + sqrt(2) and 5 - sqrt(2) are both irrational but their sum is 1 + 5 = 6.
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 numbers be added to give a non-zero rational number?
Yes. For example, the sum of 2 + √3 and 2 - √3 is 4.
