Irrational Numbers

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Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring.

i.e., Irrational numbers cannot be put in the form

where and

are some examples of irrationals.

(i) is also irrational. Its approximate value is

(ii) It is not possible to find the exact value of an irrational number.

(iii) All rational and irrational numbers can be marked on the number line.

Write two possible irrational numbers between 2 and 3.

Consider the squares of 2 and 3

and

5 and 6 lie between

lie between 2 and 3.

The required possible irrational numbers are

We can obtain infinite number of irrationals between two irrational numbers.