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Consider pi and 4 - pi.
4 - pi + pi = 4, which is clearly rational. However, both pi and 4 - pi are irrational, as you can verify.
plz to be lerning numburs Then consider pi + pi = 2pi, which is clearly irrational. The sum of two Irrational Numbers, therefore, may or may not be rational.
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Is the sum of an irrational number and rational always irrational?
Yes.
Is the sum of a rational number and an irrational number always irrational?
Yes, always.
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
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 two rational numbers is it rational or irrational?
Such a sum is always rational.
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.
Are the sum of two rational numbers rational or irrational?
They are always rational.
The sum of rational numbers and an irrational number?
It is always an irrational number.
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
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.
Sum of two irrational numbers?
Can be rational or irrational.
What is the classification of the sum rational and irrational numbers?
Irrational
The sum of a rational number and an irrational number?
Such a sum is always 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.
Is the sum of two or more rational numbers is it rational or irrational?
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
Is the sum of an irrational number and rational always irrational?
Yes.
