Oldest irrational number (2024)

FAQs

What is the oldest irrational number? ›

The first irrational number discovered was the square root of 2, by Hippasus of Metapontum (then part of Magna Graecia, southern Italy) around 500 BC. A student of the great mathematician Pythagoras, Hippasus proved that 'root two' could never be expressed as a fraction.

Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them.

Famous examples are π+e, 2e, π√2, and the Euler–Mascheroni constant γ.

✨ 3.14014001400014 is an IRRATIONAL number.

Rational numbers are those which can be written as simple fractions. The square root of 42 is 6.48074069840786. It cannot be written as a simple fraction, so it is an irrational number, not a rational number.

These measures reveal that the most irrational number, i.e. the one for which rational approximations perform the worst, is 1 plus the square root of 5 all divided by two – a figure roughly equal to 1.618. This number is already well known. It's called the "Golden Ratio".

The square root of 23 is a number, which when multiplied by itself results in the original number 23. The square root of 23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.

Answer and Explanation:

A rational number is any number that is negative, positive or zero, and that can be written as a fraction. This includes all integers, such as 13, and both terminating and repeating decimals. A decimal that is neither terminating nor repeating is an irrational number.

An irrational number is a real number that can't be written as a fraction or as the ratio of two integers. It is an infinite, non-repeating decimal that never ends and doesn't have a pattern. Irrational numbers cannot be calculated exactly and must be approximated to solve mathematical problems.

The pi is the limit! The Swiss mathematician Johann Lambert proved this around 250 years ago by showing that Pi can't be expressed exactly as the ratio of one number to another – in other words, it's an 'irrational' number that goes on forever, never repeating itself.

What is a real life irrational number? ›

Do Irrational Numbers exist in real life? Irration numbers exixt in real life and also has various examples. For an example, circumference of a circle is '2πr' is an irrational number.

Pi, or π, is probably the most famous irrational number that's known for it's never ending decimal places. We estimate it to be around 22/7, but the exact number for Pi can never be a rational number. Euler's number is another famous irrational number that starts with 2.71828182845…..and so on.

If α is a non-zero rational number, then the numbers cos(α), sin(α), tan(α), sec(α), csc(α), and cot(α) are all irrational. Furthermore, the squares of these numbers are irrational. and tan2(α) = sec2(α) − 1 = 1 cos2(α) − 1 to obtain the result for sin2(α) and tan2(α). The others follow by considering reciprocals.

The number 5.676677666777... is not a rational number because it does not have a repeating pattern. A rational number can be expressed as a fraction of two integers. It can either terminate or repeat in a pattern.

0.3333 is both recurring and non terminating - it's a rational number .

The discovery of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2.

We can prove that the square root of any prime number is irrational. So √2, √3, √5, √7, √11, √13, √17, √19 … are all irrational numbers.

There is no smallest irrational number, as irrational numbers do not follow a pattern or have a defined smallest value. In fact, there are infinitely many irrational numbers between any two rational numbers.