I came upon the following question in a recent district math test, and I have no clue how to solve it, besides using a calculator and doing some serious multiplication, but no calculators were available during the test.
Which of the following numbers is a perfect square?
(A) $\frac {14!15!}{2}$ (B) $\frac {15!16!}{2}$ (C) $\frac {16!17!}{2}$ (D) $\frac {17!18!}{2}$ (E) $\frac {18!19!}{2}$
Could somebody explain how to solve this problem step by step?
(D) is equal to $\frac{17!17! \times 18}{2} = 17!17! \times 9 = (17!\times 3)^2$