If p is the prime positive integer . Prove that √p is an irrational

1.	If p is the prime positive integer . Prove that √p is an irrational number
Answer» For any prime positive integer p, √p is an irrational number.Let us assume that √p is a rational number.Then, there exist positive co-primes a and b such that :-√p = a/bp = a²/b²b²p = a²p divide a²p divides a.a = pc ( positive integer c. )Now, b²p = a²b²p = p²c²b² = pc²p divide b²p divides bTherefore, p/a and p/bThis contradicts the fact that a and b are co-primes.

Discussion