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Is a rational number is a rational expression?
Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.
Is 2 thirds a rational number?
Yes because any number that can be expressed as a fraction is a rational number
How is the sum of a rational and irrational number irrational?
This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written as p / q, where "p" and "q" are whole numbers (this is basically the definition of a "rational number"). Then, the square root of 2, which is equal to the sum minus 1, is: p / q - 1 = p / q - q / q = (p - q) / q Since the difference of two whole numbers is a whole number, this makes the square root of 2 rational, which doesn't make sense.
Find two irrational numbers whose sum is a rational number?
(pi - 1) and (2 - pi) Sum = (pi - 1 + 2 - pi) = 1
Is 18 out of 2 rational?
Yes, any number that can be expressed as a fraction is rational. Since 18 out of 2 is the same as 18/2, it 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.
Is the sum of two rational numbers a natural number?
Sum of two rational numbers might be a natural number (1/2 + 1/2), but mostly it's just another rational number (1/2 + 1/3). So answer is no.
Can you add an irrational number and a rational number?
Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.
Is the square of 2 rational number?
Yes, the square of any rational number is also a rational number.The square root of 2 is not a rational number.
How do you know that the sum of (-2 34) and 59 rational?
Because both of those numbers are rational. The sum of any two rational numbers is rational.
Is 2 an irrational number?
No. Any number that has a finite number of digits if RATIONAL.
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 2 squared rational or irrational?
The square of any rational number is also rational.
Is a rational number is a rational expression?
Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.
Is 2 thirds a rational number?
Yes because any number that can be expressed as a fraction is a rational number
How is the sum of a rational and irrational number irrational?
This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written as p / q, where "p" and "q" are whole numbers (this is basically the definition of a "rational number"). Then, the square root of 2, which is equal to the sum minus 1, is: p / q - 1 = p / q - q / q = (p - q) / q Since the difference of two whole numbers is a whole number, this makes the square root of 2 rational, which doesn't make sense.
Give Two different irrational numbers whose sum is a rational number?
1 + pi, 1 - pi. Their sum is 2.
