Let p be a positive prime and prove that the root P is irrational

Let p be a positive prime and prove that the root P is irrational

Let √ p be a rational number, then √ P can be written as a fraction. Let √ P = m / N, where m and N are coprime positive integers, then: P = m ^ 2 / N ^ 2, that is, p * n ^ 2 = m ^ 2. From the above formula, we can see that m ^ 2 has a divisor P, that is, M has a divisor P, that is, let m = PK, where k is a positive integer, then: P * n ^ 2 = m ^ 2 = (PK) ^ 2 = P ^ 2 * k ^ 2, that is, n ^ 2 = P * k ^ 2 from above

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