Question

Prove that root 3+root5isirrational number by contridiction methods

Answer 1

heya,!!!
let us suppose that that (√3+√5)is rational no.
let [√3+√5] =a where a is rational no.

then ,√5^2=[a-√3]^2-----1)
on squaring both sides of (1)

=)5=3+a^2-2√3a

=)-3-a^2+5=-2√3a

=)2-a^2/2a=-√3

=)√3=a^2-2/2a

this is impossible as the right hand side is rational √3 while is rational

this is contradiction.

since the contradiction arises by assuming that (√3+√5) is rational

hope it help you

@rajukumar☺

Answer 2

I hope it may help you