Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
Pi is the value of a circle's circumference divided by its diameter and its true value has never been discovered because it is an irrational number
An irrational number.
There is no first irrational number. Irrational numbers are infinitely dense which means that there are infinitely many of them in any interval. So if any number laid claim to being the first, there would be infinitely many that would be between 0 and that number. Each one of them would then have a better claim to be "first".
Irrational numbers were known in India around 7th Century BCE but there existence as a different class of number but they had not proved their existence. That is sometimes attributed to Hippasus, a Greek philosopher of the Pythagorean school in the 5th Century BCE.
Pythogora
Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.
The square root of negative 36 is an imaginary number and therefore not an irrational number. For a number to be irrational it must first be real.
William Shanks is not known to have created any number - rational or irrational. He did calculate pi to a greater degree of accuracy then previously but the number pi had been discovered around 4 thousand years before Shanks. Therefore it can hardly be said that he discovered it.
No one has ever shown that 2 is an irrational number because it is rational.
Pi is the value of a circle's circumference divided by its diameter and its true value has never been discovered because it is an irrational number
Irrational numbers have been known since very early times. For example, it was recognised that the length of the diagonal of a unit square was not a rational number. There is, therefore, no specific date.
An irrational number.
There is no first irrational number. Irrational numbers are infinitely dense which means that there are infinitely many of them in any interval. So if any number laid claim to being the first, there would be infinitely many that would be between 0 and that number. Each one of them would then have a better claim to be "first".
No. The sum of an irrational number and any other [real] number is irrational.
The sum of a rational and irrational number must be an irrational number.