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# Is the sum of e and Pi irrational or rational?

Updated: 11/3/2022

Wiki User

11y ago

According to several sources such as Wikipedia and Wolfram Alpha, this is an open question. In fact, there is no pair of non-zero integers m and n for which it is known whether mπ + ne is irrational or not.

Wiki User

11y ago

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Q: Is the sum of e and Pi irrational or rational?
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### Example for sum of a rational number and irrational number?

example for sum of rational numbers is 1/3 + 1/5 Example for sum of irrationals is Pi + e where e is is base of natural log Another is square root of 2 + square root of 3.

### Is pi divided by e rational?

A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.

### Can you add two irrational numbers to get an irrational number?

Yes.An example:1 + 2^(0.5) is an irrational number,1 -(2^(0.5)) is also a irrational number.(1 + 2^(0.5)) + (1- 2^(0.5)) = 22 is a rational number.Therefore the sum of two irrational numbers can equal a rational number.But this is not the question. Can you add two irrational numbers to get another irrational number. Yes. Almost all additions of two irrational numbers result in another irrational number. For instance pi (3.141...) and e (2.718...) are both irrational, and so is their sum. In some sense you have to work quite hard to make the sum not irrational (i.e. rational) because the two decimal expansions have to conspire together either to cancel out or to give a repeating decimal.Actually, pi+e may or may not be irrational. This hasn't been proved either way. See: http://en.wikipedia.org/wiki/Irrational_number (under "Open Questions")Yes. For example, pi + (-pi) = 0.any number that is a non-terminating decimal is called an irrational number.

### Can you subtract 2 irrational numbers to get a rational number?

Yes. Example: pi - pi = 0.You can even subtract two different irrational numbers to get a rational number.For example: e - (e - 1) = 1 or &Phi; - (1/&Phi;) = 1.

### Is 012131415. rational or irrational?

If it would never end, then it is irrational e.g. 10/3 = 3.33333333... etc.. if it ends it's rational e.g. 1000/8 = 125 other irrational numbers: pi, e

### Which numbers is not rational?

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

### Examples of irrational and rational numbers?

5, -7.986543, 37/91, sqrt(64), 193 are all rational. sqrt(2), pi, e, cuberoot(32) are all irrational.

### Is e to the pi rational?

e^pi ~ 23.14069.............., not rational

### Why do you use irrational nombers?

There are many common numbers in mathematics which are not rational. Two of the most important numbers in mathematics are pi and e: both are irrational.

### Can you add a rational number and an irrational number and get a rational number?

No, the result is always an irrational number. In more advanced math it is possible to add an infinite amount of rational numbers by way of Taylor Series and get an irrational number. This is how numbers like "Pi" and "e" are derived.

### How are irrational numbers used in world?

There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.

### Is every real number also a rational number?

No. "Pi", "e", and the square root of 2 are all real and irrational.