Find the remainder when ( 1! )^2 + ( 2! )^2 + ( 3! )^2 + ……… + ( 100! )^2 divided by 100.

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.