jmc

First we find the prime factorization of 735, which is $3\cdot 5\cdot 7^2$. In order to make a perfect square, we need another factor of 3 and another factor of 5. So if $a=15$, we have $ax=(3\cdot 5)(3\cdot 5\cdot 7^2)=3^2\cdot 5^2\cdot 7^2$. That means $\sqrt{ax}=3\cdot 5\cdot 7=\boxed{105}$.