Question

Examine whether underoot 2 is rational or irrational numbers

Answer 1

I think root 2 Is a irrational no because it is non repeating and non terminating no.. in short we can express it in point .. but rational no requires p÷q form and q Should not be 0 ..

hope it helps you but I am not sure about this answer ...

Answer 2

heya,

if possible √2 be rational and simplest form is p/q
then ,a and b are integer it have no common factor other than 1 and bis not equal to 0.

then ,
√2=a/b =)2 =a^2/b^2( squaring on both side)

2b^2=a^2

2 divides a^2
and so ,(2 divides 2b^2 )

=) 2 divides a ,but 2 is prime and divides by b^2 =) 2 divides b .

let a=2c for some integer c .

putting a =2c in (1) we get .

2b^2=4c^2 =)b^2=2c^2
=)2 divides b^2 ( so,2 divides 2c^2 )
=)2 divides b

so, 2 is prime and 2 divides b^2 =)2 divides b

thus two is common factor of a and b .

but this is contradiction fact that a and b have no common. common factor other than 1 .

the contradiction arises by assuming that √2 is rational .
hence √2 is irrational..


hope it help you


@rajukumar.