If we talk about irrational numbers, then in mathematics, the irrational numbers are all the real numbers, or the latter bring the numbers constructed from the ratio of integers or we can say that an irrational number is a number that cannot be expressed as a fraction for any integer. An irrational number is a number that is not rational. So it can not express as like fraction p/q.
Every transcendental number is irrational.
The value that we get is actually not terminating. Also, there is no pattern in the digits after the decimal. These kinds of numbers are called irrational numbers.
Irrational Number does not terminate, nor do they repeat, i.e, do not contain a subsequence of digits, the repetition of which makes up the tail of the representation.
π = 3.1415926535897932384…
√2 = 1.14121356230951…..
(2 + √3)
Above example, the value that we get is actually not terminating. Also, there is no pattern in the digits after the decimal.
A floating-point number is not irrational Number when:
1. The limited number of digits after the decimal point.
For example, 5.4321.
2. The infinitely repeating number after the decimal point.
For example, 2.333333…
3. The infinitely repeating pattern of numbers after the decimal point.
For example, 3.151515…
Examples of irrational numbers:
1- As we know that Pi, is determined by calculating the ratio of the circumstances of a circle to the diameter of that same circle and it is one of the most common irrational numbers whose value is 3.14.
2-The golden ratio, written as a symbol is an irrational number that begins with 1.618033…………
3- e, known as Euler number, It is an irrational number
Properties of Irrational Number
1. The product and division of two irrational numbers can be rational or irrational number.
For example: √2 x √2 = 2 (rational number)
2. The division of two irrational numbers can be rational or irrational number.
For example: √2 ÷ √2 = 1 (rational number)
3. The result of an addition of irrational numbers need not be an irrational number
For example: (5 + √2) + (4 – √2) = 5 + √2 + 4 – √2 = 9 (rational number)
4. The result of Subtraction of irrational number need not be an irrational number
For example: (5 + √2 ) – (3 + √2) = 5 + √2 – 3 – √2 = 2 (rational number)
If you have any doubts related to this topic, you ask into the comment. If you have any problem in mathematics you can post your problem in the comment section. You will get the answer.
I hope you have learned it properly.