I got the same answer as Winga, but I wrote it as:

t_{H} = sqrt(A_{0}) * (1/k) * (2 - sqrt(2))

When dealing with factors of sqrt(2), they can usually be written in all kinds of different looking ways that aren't obviously the same until you do some calculations to check.

One hint, madscientist, that your first answer wasn't right, is that your half-life was proportional to k, the rate constant. That meant that, the higher the rate, the longer the half-life. It should be the other way around, so proportional to (1/k) makes more sense.

BTW - Since you seem to be doing this for multiple reaction orders, it isn't that much harder to calculate the result for an arbitrary reaction order n, and then keep re-using this result. There is one 'special case', it is the usual one of n=1.