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If x is a rational number and y is an irrational number what can you say about x plus y?
Wiki User
∙ 9y ago
It is irrational.
Wiki User
∙ 9y ago
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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.
If x is a rational number and y is an irrational number then can you say about x plus y?
please rephrase or grammar-check your question.
Is 0.83 an irrational number?
I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.
When can you say that a given real number is irrational?
A real number is an irrational number if it cannot be expressed as a fraction a/b, where a and b are integers. Most real numbers are irrational. The most well known irrational numbers are π and √2. The inverse condition are called the rational numbers.
Which irrational number is closest to 6?
Irrational numbers are infinitely dense. That is to say, between any two irrational (or rational) numbers there is an infinite number of irrational numbers. So, for any irrational number close to 6 it is always possible to find another that is closer; and then another that is even closer; and then another that is even closer that that, ...
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.
If x is a rational number and y is an irrational number then can you say about x plus y?
please rephrase or grammar-check your question.
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.
Is -11.7 an irrational number?
NO it is not irrational, that is to say it IS rational. If you can write a number as ratio of integers, it is rational. -11.7 can certainly be written as a ratio of integers.
Is 0.83 an irrational number?
I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.
What two irrational numbers make a rational number?
The simplest example (of infinitely many) is probably the squareroot of two multiplied by itself equals two. Take any rational number, say 4.177 and divide it with any irrational number, say the square root of 13, and you will get a new irrational number. The product of your two irrational numbers now make a rational number.
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.
Are rational and irrational numbers in the set of real numbers?
Yes. Together, they make up the entire set of real numbers. That is to say, any real number is either rational or irrational.
Is 2.5 an irrational number?
No. If a number is irrational, it continues endlessly without a pattern. Since 2.5 stops at 5, it is rational; but if it were, say, 2.573583..., it would be irrational. Also, it can be written as the fraction 25/10, or 5/2.
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.
A short note on square root of rational number?
Square root of a rational number may either be rational or irrational. For example 1/4 is a rational number whose square root is 1/2. Similarly, 4 is 4/1 which is rational and the square root is 2 which of course is also rational. However, 1/2 and 2 are rational, but their square roots are irrational. We can say the square root of a rational number is always a real number. We can also say the rational numbers whose square roots are also rational are perfect squares or fractions involving perfect squares.
What is an irrational number means?
a number that cannot be expressed as a fraction or a ratio. Formally, we say a number is rational if it can be written in the form p/q where p and q are integers. If it cannot be written this way, it is irrational.
