A practical use for a geiger counter is to locate low level radioactive sources in and around the household, then move them from your living space. Examples of radioactive materials that can be found inside the house include rock/mineral colections, certain pottery glazes, gas lantern mantles, antique watch/radio dials, certain welding rods, and radon gas.
Common smoke detectors typically contain a tiny piece of radioactive americium, which emits alpha particles. Very little alpha radiation eminates from the detector because it is blocked by a metal shield. The life-saving capabilities of smoke detectors far outweigh the negative effects of the radioactivity.
Keep in mind, there is, and has always been, a fair amount of normal background radiation from radioactive minerals in the ground, and radon gas. Above-ground atomic testing in past years has increased the background radiation levels somewhat, but this is mostly a concern for people living close to the test sites.
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