Irrational Numbers- A Crucial Component Of The Number System

Irrational Numbers- A Crucial Component Of The Number System

Those real numbers that cannot be expressed as a ratio are called irrational numbers. Irrational numbers, on the other hand, are real numbers that are not rational numbers. Hippasus, a Pythagorean philosopher from the 5th century BC, found irrational numbers. In the end, his theory was mocked and he was dumped into the water. This website will help you better comprehend the notion of irrational numbers, and you won’t end yourself in the water. If you understand the idea, then you will also understand the irrational number listing, the distinction between irrational and rational numbers, but whether or not irrational figures are actual numbers.

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics (from the prefix in- assimilate to ir- (negative prefix, privative) + rational). Meaning that the ratio of two integers does not apply to non-rational numbers. It is also known as incommensurability when the ratio of the lengths of two line segments is an irrational number. This means that the two line segments do not share a “measure” in common. Other irrational numbers include the circle’s circumference/diameter ratio, Euler’s number e, and the square root of two. Even perfect squares have an irrational square root.

Properties of Irrational Numbers

It is possible to identify irrational numbers from a set of real numbers by using properties of irrational numbers. Irrational numbers have a lot of interesting features.

  • Irrational Numbers are termed as actual or real numbers.
  • Any two Irrational numbers can be multiplied by any rational number which is non-zero and their product will be equal to the irrational number. Take for example an irrational number is y and the rational number is z then their product will be yz which will be irrational.
  • Any two irrational numbers and rational number’s addition will be equal to an irrational number only. Take for example, if an irrational number when added to a rational number b will be equal to a+b which will be an irrational number.
  • In any case the sum, product, difference and division of two irrational Numbers can be rational or irrational, it varies.
  • Irrational Numbers comprises both non-terminating and non-recurring decimals.
  • The LCM of two irrational Numbers might exist in some cases.

How Can You Identify an Irrational number?

Unknown irrational numbers cannot be represented in the form of p/q, where P and Q are integers and Q is greater than zero. Unrealistic numbers include, for example, 5, 3, and so on. Numbers that may be written as p/q, where q is an integer and p is an integer, on the other hand, are rational numbers.

Symbol of Irrational Numbers

Irrational numbers have a special symbol. Let’s look at other sorts of numbers first.

“N” stands for “Natural numbers”

“I” stands for “Imaginary Numbers”

“R” stands for “real numbers.”

“Q” stands for “Rational Numbers.”

Rational and irrational numbers are both included in real numbers. Rational numbers may be generated by subtracting real numbers (R) from the rational numbers (Q) (R). Another way to write this is (R\Q). Hence Numerical Insanity Q’ is the symbol.

Irrational Numbers In The Form Of Sets

You can get a set of irrational numbers by putting a few irrational numbers in brackets. Irrational numbers have certain features that allow them to be identified.

There exist irrational numbers in all non-perfect square roots. Irrational numbers such as 2, 3, 5, 8, the Golden ratio, and Pi are well-known. {e, ∅}

Prime numbers have irrational square roots.


This article is an attempt to cover the important concepts of irrational numbers. It explains to the readers the important terminologies related to irrational numbers. It is a very important topic from the examination perspective. Many questions have been asked in competitive examinations on this particular topic. Students can take the help of math worksheets from the house of Cuemath to gather more information about this topic.


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