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An irrational number is a real number that cannot be expressed as a ratio of two integers, x and y, where y>0.

In 1761, Johann Heinrich Lambert proved that pi is irrational. His proof and alternatives by other mathematicians can be found at the attached link.

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Q: What is an irrational number and why is pi an irrational number?
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Related questions

Is 2 pi a rational number?

No, since Pi is an irrational number, 2(pi) would still be irrational.


Is negative pi rational or irrational?

-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.


Is pi a recurring decimal a terminating decimal or an irrational number?

Pi is an irrational number


What is pi an irrational number?

Yes, it is an irrational number.


Is pi plus pi a rational or irrational number?

It is irrational, just like pi


Why is 10 pi irrational?

A non-zero rational number (10) multiplied by an irrational number (pi) is always irrational.


Why is PI a rational or irrational number?

pi is an irrational number. It is irrational because it cannot be expressed as a ratio of two integers.


Why pie is a rational or an irrational number?

First of all 'pi' is spelled as 'pi' . NOT 'pie' ; that is the meat pie of apple pie that you eat. 'pi' is the small case classical Greek letter 'p' and mean 'proportion'. It is the proportional constant between a circles diameter and circumference. 'pi' is an IRRATIONAL number. Casually this means, that the decimal digits go to infinity, and the digits are NOT in a any regular order. . More formally 'irrational' means that you cannot form an exact ratio from it's decimal digits. pi= 3.14 , 3.1416, 3.14592654, 22/7 are all approximations of 'pi'. Super . Duper Computers have calculated 'pi' to billions of places and still going. !!!!!


Is the square of pi a rational or irrational nuymber?

The square of pi is an irrational number.


Is the ratio of the circumference and diameter of a circle is an irrational number?

That's the number pi, and yes, it is irrational.


Why is pi a rational number?

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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.