Question

Prove that 7-2√2 is irrational

Answer 1

                           Prove by contradiction method
let 7-2√2 be rational  then 7-2√2=r (where r ∈ rational numbers)

*   7-2√2=r
                        (squaring on both sides)
*     (7-2√2)²=r²

*  7² -2(7)(2√2)+(2√2)²=r²

*                49-28√2+8=r²

*                    57-28√2=r²

*                         -28√2=r²-57

*                             √2=r²-57÷28

According  to solution √2=r²-57÷28 which means √2 is rational.But it contradicts the fact that √2 is irrational.Hence 7-2√2 is irrational.