0
The sum or the difference between two Irrational Numbers could either be rational or irrational, however, it should be a real number.
Add your answer:
Earn +20 pts
The difference of two irrational numbers is an irrattinal number?
The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.
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 two irrational numbers necessarily irrational?
Yes, as long as the two are not mutual resiprocals.
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 an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
The difference of two irrational numbers is an irrattinal number?
The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.
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.
Sum of two irrational numbers?
Can be rational or irrational.
What is the classification of the sum rational and irrational numbers?
Irrational
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
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 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 of two irrational numbers?
It may be a rational or an irrational number.
The sum of rational numbers and an irrational number?
It is always an irrational number.
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 irrational numbers also an irrational number?
Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.
