Question

show that 3 + root 2 is irrational given that root 2 is irrational​

Answer 1

Answer:

let us assume that 3+√2 is rational.if it is rational then there must exist two integers 3+√2=a/b.if a and b have a common factor other than we divide by the common factor to get 3+√2 = a/b

3+√2=a/b

3/1-a/b=√2

3b-a/b=√2

3b-a/b is rational,√2 is rational.

this is our contradiction.this contradiction arise due to our wrong assumption.so3+√2 is an irrational number