Question

prove that 3 + 2 root 5 whole bracket cube is an irrational number​

Answer 1

let us think that it is rational so it will be in the form of p/q where p n q are co primes.

so it will be in the form of p/q=3+2root5

now taking 3 on lhs. we get p/q-3=root 5

now lhs is a rational no. so rhs will also be rational no. but the contradiction facts that root 5 is an irrational no. so 3+2root 5 is irrational so our aasumption was wrng that it is rational

hence proved