The five-digit positive integer $15 A B 9$ is a perfect square for some digits $A$ and $B$. What is the value of $A+B$ ?
Since $120^{2}=14400$ and $130^{2}=16900$, then $15 A B 9$ is the square of an integer between 120 and 130 .

Since $15 A B 9$ has a units digit of 9 , then it is the square of an integer ending in 3 or 7 .

Note that $123^{2}=15129$ and $127^{2}=16129$, then $A=1$ and $B=2$, so $A+B=3$.

ANSWER: 3