Let p be a prime number Show that p is not a perfect squareS

Let p be a prime number. Show that p! is not a perfect square.

Suppose that p is a prime number

Then p will not repeat in any of the other factors of p!

This implies that p! cannot be a perfect square.

Hence if p is a prime implies that p! is not a perfect square.

Example:

3!=3*2*1=6 is not a perfect square

5!=5*4*3*2*1=120 is not a perfect square