0
Why does any real number must be either a rational number or an irrational number?
Wiki User
∙ 9y ago
It is due to the fact that the set of real numbers is defined as the union of the rational and Irrational Numbers.
Wiki User
∙ 7y ago
Add your answer:
Earn +20 pts
May the sum of a rational and an irrational number only be a rational number?
No. In fact the sum of a rational and an irrational MUST be irrational.
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
When you take the square root of an irrational number will the outcome be rational or irrational?
The square root of an irational number must, itself, be irrational.
Why is the productof a non zero rational number and an irrational number is irrational?
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational.Then, dividing both sides of the equation by A gives B = A/C.Now, since A and C are both rational, A/C must be rational.Therefore you have B (irrational) = A/C (irrational).Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration or, it must be irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Is 0.555555 both rational and irrational rational neither rational nor irrational irrational?
No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
May the sum of a rational and an irrational number only be a rational number?
No. In fact the sum of a rational and an irrational MUST be irrational.
What product is true about the irrational and rational numbers?
The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.
The sum of a rational number and an irrational number?
Such a sum is always irrational.
Are real numbers rational and irrational?
The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.
Why the area of a circle with a rational radius must be an irrational number?
It the radius is r then the area is pi*r*r - which is pi times a rational number. pi is an irrational number, so the multiple of pi and a rational number is irrational.
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
When you take the square root of an irrational number will the outcome be rational or irrational?
The square root of an irational number must, itself, be irrational.
Why does a rational number plus an irrational number equal an irrational number?
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
Why is the productof a non zero rational number and an irrational number is irrational?
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational.Then, dividing both sides of the equation by A gives B = A/C.Now, since A and C are both rational, A/C must be rational.Therefore you have B (irrational) = A/C (irrational).Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration or, it must be irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
