Question

prove that 3+root 2is an irrational number​

Answer 1

let us assume that 3+root 2 is a rational number and suppose 3+root 2 =a/b (where a and b are coprime )

now, 3+ root 2 =a/b

=root 2 =a/b -3

since a/b-3 is an integer so a/b-3 is a rational number.

but a/b-3=root 2

since root 2 is an irrational number so we conclude that our assumption that 3+root 2 is a rational number is wrong.

hence we come to the conclusion that 3+root 2 is an irrational number.