In mathematics, there are various types of numbers such as real numbers, natural numbers, whole numbers, negative and positive numbers, and so on. Similarly, irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction. Irrational numbers can also be defined as real numbers which cannot be written or represented in the form of p/q or a/b where q or b is not equal to zero. The opposite of irrational numbers is rational numbers. Those numbers can be expressed in the form of simple fractions i.e., real numbers or in the form of p/q where q is not equal to the number 0. Some examples of rational numbers are as follows: ¾, ⅚, 4, 8, etc. Some examples of irrational numbers are as follows: √5, √8, √3, etc. In this article, we will try to cover some basic aspects of irrational numbers such as properties of these numbers, comparison from rational numbers, and do a brief analysis about them.
As mentioned above, irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction. Let us look into the properties of these numbers. Some of them are mentioned below:
- If we add an irrational number and a rational number, the resultant value will always be a rational number. For example, ‘x’ is an irrational number, and ‘y’ is a rational number, then x + y = z which is a rational number. Therefore, the sum of a rational and irrational number is equivalent to a rational number.
- The arithmetic operation of multiplication with a number that is irrational and with a rational number that is non-zero in nature will provide you with an irrational number.
- The least common divisor or multiple of a number that is irrational may exist or may not exist.
- If we add or multiply two irrational numbers, the resultant value always comes as a rational number. For example, when two irrational numbers such as √5 and √5 are multiplied the answer comes = 5 which is a rational number.
- You may observe that the set of the number which is rational may be closed during the process of multiplication. But, in irrational numbers, the contrary happens.
In the next few points, we will carry out the comparison of rational and irrational numbers.
- Irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction whereas rational numbers can be represented in the form of a simple fraction.
- The irrational numbers cannot be expressed in the form of a/b or p/q where b or q is not equal to zero whereas the rational numbers can be written in the form of p/q where q is not equal to zero.
- Some examples of rational numbers are as follows: ¾, ⅚, 4, 8, etc. Some examples of irrational numbers are as follows: √5, √8, √3, etc.
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