Question

root 5 is a irrational number prove that 3root7+4 is also irrational

Answer 1

let us consider3√7 + 4 be a rational no.
3√7+4=p/q where p and q are integers and q is not equal to 0
3√7+4=p/q
3√7=p/q-4
√7=(p-4q)/3q
as p-4q/3q is a rational no. but this contradicts the fact that √7 is an irrational no.
this contradiction has arisen due to the wrong assumption that √7 is an rational no.
so , √7 is an irrational no.