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No. 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.
Jasen Runte
Wiki User
∙ 7y agoThe square root of 2 is irrational; this is proven in many high school algebra books. The same proof can be applied to any natural number that is not a perfect square; that is, the square roots of 3, 5, 6, 7, 8, 10, 11, 12, ... are all irrational.
Wiki User
∙ 14y agoIt may be either. Examples:
pi + pi = 2pi (irrational).
pi + (5-pi) = 5 (rational).
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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 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.
Is two thirds a rational or an irrational number?
2/3 is rational. 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 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.
Can 2 irrational numbers add together to form a rational?
Yes. For example: a = 10 - pi b = pi Both are irrational; the sum a + b is 10.
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 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.
Can 2 irrational add to an irrational number?
Yes. The sum of two irrational numbers can be rational, or irrational.
Erika knows that when you add two rational numbers you get ar rational number therefor she concludes that the sum of two irrational numbers is irrational prove her wrong?
1+sqrt(2) and 1-sqrt(2) are both irrational but their sum, 2, is rational.
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.
Can the sum of two irrational numbers ever be rational?
Sure. For example, the sum of:root(2) and: - root(2) is zero, which 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.
Can you add irrational numbers to get a rational number?
Yes. Consider 4+sqrt(2), and 3-sqrt(2). Both are irrational numbers. Their sum is 7.
Is the sum of two POSITIVE irrational numbers ALWAYS irrational?
No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.
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.
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.
Is the sum of 2 irrational numbers always rational?
No. 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.
