Question

Prove that 7+3√3 is irrational

Answer 1

Answer:

let us assume to the contrary that 7+3root 3 is rational then their exists two coprime integers p and q (q not equal to zero ) such that 7+3root3= p/q .therefore 7+3root3=p/q implies that root 3= (p/q - 7 )x 3 . since p and q are coprime integers therefore (p/q-7)x3 is a rational no. but this contradicts the fact that root 3 is irrational . this contradiction has asrisen due to our incorrest assumption that 7+ 3root3 is irrational .therefore 7+3root3 is irrational . hence proved .