Question

prove that 3+7√5 is irrational number.
Shot form

Answer 1

we know that 3 is rational and 7root 5 is irrational so rational +irrational =irrational...

Answer 2

let 3+7root5 is a rational number
a/b=3+7root5
7root5=a/b-3
root5=a/7b-3
root5=a-21b/7b
in LHSroot5 is irrational but in RHS a-21b/7b is rational number so our acception went wrong so 3+7root5 is irrational number