Question

what is irrational number​

Answer 1

Answer:

The irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. ... For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.

Answer 2

Hi mate

Here is ur answer ✏

$\huge\mathfrak{\underline{\underline{\red{Answer}}}}$

$\bf\bold{\blue{Irrational \: \: number}}$

Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.

Irrational numbers are expressed usually in the form of R\Q, where the backward slash symbol denotes ‘set minus’. it can also be expressed as R – Q, which states the difference of set of real numbers and set of rational numbers.

The calculations based on these numbers are a bit complicated. For example, √5, √11, √21, etc., are irrational. If such numbers are used in arithmetic operations, then first we need to evaluate the values under root. These values could be sometimes recurring also.

How do you know a number is irrational?

The real numbers which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0 are known as irrational numbers. For Example √ 2 and √ 3 etc. are irrational. Whereas any number which can be represented in the form of p/q, such that, p and q are integers and q ≠ 0 is known as a rational number.

Properties

The following are the properties of irrational numbers:

• The addition of an irrational number and a rational number gives an irrational number. For example, let us assume that x is an irrational number, y is a rational number, and the addition of both the numbers x +y gives a rational number z.
• Multiplication of any irrational number with any nonzero rational number results in an irrational number. Let us assume that if xy=z is rational, then x =z/y is rational, contradicting the assumption that x is irrational. Thus, the product xy must be irrational.
• The least common multiple (LCM) of any two irrational numbers may or may not exist.
• The addition or the multiplication of two irrational numbers may be rational; for example, √2. √2 = 2. Here, √2 is an irrational number. If it is multiplied twice, then the final product obtained is a rational number. (i.e) 2.
• The set of irrational numbers is not closed under multiplication process, unlike the set of rational numbers.