CBSE Class 10 Answered
We know by the Fundamental Thm of Arithmetic that
every composite number canbe factorised in a unique way as a product of prime numbers.
Consider a as the product of prime numbers
Now, the Fundamental Theorem tells us that since p divides a squared, so p must be one of the prime factors of a squared. But from the 'unique' factorisation part of the theorem we can say that the only prime factors of a squares are p1, p2, p3... pn.
So p must be one of these numbers.
Since a is the product of these numbersp1,p2..pn, so p must divide a.This proves it.
You can try this by giving values to a and p and check it. It will help you understand it even better.