Its a matter of what type of radiation you are talking about.
There is background radiation every where, go out the garden and check the rocks, or your granite bench top.
Radiation is with us in every day life and a gadget that goes beep, buzz, whistle, and farts, dont tell you a lot unless you understand what it is you are looking at and what form of radiation you are dealing with.
For interest all early watch faces was painted with a beta radiation compound so they glowed in the dark, all is fine with a glass or plastic layer over the face of the watch. but in early years this was hand applied with a brush and the women (normally due to their finer motor skills) would point the brush in their mouth to get a fine tip, this lead to mouth and throat cancer, but had no effect on the user as the watch face blocked the radiation.
I was trained and licensed to handle radioactive material for use in oilfield applications from sources to trace materials, to start with i was **** scared of this stuff, but with education and understanding (plus respect) radiation is not a instant killer and as bad as we all first think, its like electricity it can kill you but understood and respected it is quite safe.
Many products i worked with had a 300 year half life and needed respect when handled, but are safe when used correctly.
The first thing you learn is just how much natural radiation is around us in everyday life (background radiation) and its all comes down to timed exposure no matter what the source is.
Dont be scared of your tiles, or the rocks in your garden, as it would take years of constant contact to emit enough radiation to cause an effect, and even then you would want to have your underpants lined with these materials to be of a dangerous level.
If you want a source to be concerned about go check you microwave.
Radiation is a natural part of our lives and its only the high concentrations in gama form that is of most danger.
Pete.