jmc

First, we would like to determine if 49 can be written as the sum of two perfect squares.

$49-1=48$, which is not a perfect square.

$49-4=45$, which is not a perfect square.

$49-9=40$, which is not a perfect square.

$49-16=33$, which is not a perfect square.

$49-25=24$, which is not a perfect square.

We don't need to check any other squares, as $25>\frac{49}{2}$.

Now, we check to see if there are three perfect squares that sum to 49. With a little work, we see that $49=4+9+36$. Thus, the fewest number of perfect square terms that can be added together to sum to 49 is $\boxed{3}$.