jmc

In order for a number to be a multiple of 9, the sum of its digits must be divisible by 9. Since $225=15^2$, the largest perfect square that is less than 225 is $14^2=196$. However, $1+9+6=16$, which is not divisible by 9. The next largest perfect square less than 225 is $13^2=169$, but again, $1+6+9$ is not divisible by 9. Continuing, $12^2=144$. The sum of the digits of $144$ is $1+4+4=9$, so $\boxed{144}$ is the largest perfect square less than 225 that is a multiple of 9.