Q. 175.0( 1 Vote )

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

(ii)

(iii)

(iv)

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 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.

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