Examine, whether the following numbers are rational or irrational:
(i)
(ii)
(iii)
(iv)

(i)

using (a  +  b) ² =a ² +  2ab  +  b ²

It cannot be expressed as ratio of two integers and value of √2=1.41421356 … which is non termination non repeating.

Hence, it is an irrational number.
(ii)

=2/1

Using (a-b)(a  +  b)=a ² -b ²

It can be represented in form p/q (p=2, q=1) where q≠0 and p;q have no common factor other than 1.

Hence, it is a rational number.

(iii)

Using (a  +  b) ² =a ² +  2ab  +  b ²

It cannot be expressed as ratio of two integers and value of √6= 2.449489742… which is non termination non repeating.

Hence, it is an irrational number.

(iv)

Rationalising with √2

It cannot be expressed as ratio of two integers and value of √2= 1.41421356… which is non termination non repeating.

Hence, is an irrational number.