$200/$65.89 = 3 packs of 24 AA batteries

Nest smoke detectors take 6 batteries each https://support.google.com/googlenest/answer/9297548?hl=en#:....

72 batteries / 6 batteries/device = approximately 12 smoke detectors (could be 9, 10, or 11)

We have 6 First Alert smoke detectors that are connected together but don't use WiFi. There's 1 in each bedroom and a couple left over for key places.

Using 12 smoke detectors is being very careful to cover every space or a big house. Or both.