2023 AMC 12A 第 3 题

A perfect square is divisible by $5$ exactly when its root is a multiple of $5$

The squares are $(5k)^2$; find how many satisfy $(5k)^2\lt 2023$

A perfect square is divisible by $5$ only if its root is, so the squares are $(5k)^2=25k^2.$

Since $44^2=1936\lt 2023$ $\lt 2025=45^2,$ the root can be $5,10,\ldots,40,$ which is $k=1$ through $8.$

Thus, the correct answer is A.