Q. 194.5( 2 Votes )

Examine whether the following numbers are rational or irrational:
(i)

(ii)

(iii)

Answer :


(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 terminating and non-repeating
Hence, it is an irrational number.

(ii)

=6/1

Using (a - b)(a  +  b)=a 2 -b 2

It can be represented in form p/q (p=6, q=1) where q≠0 and p and q have no common factor other than 1.

Hence, it is a rational number.

(iii)

Rationalising with √3

It cannot be expressed as the ratio of two integers and value of √3= 1.73205080… which is non-terminating and non-repeating.

Hence, it is an irrational number.

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