Question

√3 is rational or irrational. explain

Answer 1

Irrational because it can't be expressed in ratio form

Answer 2

Hey there!!!

√3 is an irrational

=>> If possible , let √3 be rational and let it's simplest form be a/b.

Then , a and b are integers having no common factor other than 1, and b is not equal to 0.

Now , √3 = a/b => 3 = a² / b²

=> 3b² = a²

=> 3 divides a²

=> 3 divides a

[ 3 is prime and 3divides a² => 3 divides a ]

Let a = 3c for some integer c.

putting a = 3c in (i) , we get

3b² = 9c => b² = 3c²

=> 3 divides b² [ 3 divides 3c² ]

=> 3 divides b.
[ 3 is prime and 3 divides b² => 3 divides b]

Thus, 3 is a common factor of a and b.
but , this contradicts the fact that a and b have no common factor other than 1.

The contradiction arises by assuming that √3 is rational wrong.

Hence, It is √3 an irrational.

Hope it helped!!!☺️