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This is a hypothetical question I'm asking as a SF writer, and the time setting would be approximately 2,250 AD.

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    $\begingroup$ Welcome to the site @MikeAckerman. Often world building questions are closed but this is a good science based one and I suspect you'll get good answers. $\endgroup$ – GdD Feb 15 '18 at 10:04
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    $\begingroup$ Thank you for asking this! I had wondered this myself but never thought to post the question. I've heard so much about Jupiter's ferocious radiation environment that I always envisioned the answer would be "miles" or "you can't." I'm pleasantly stunned by PearsonArtPhoto's elegant answer. $\endgroup$ – Kengineer Feb 15 '18 at 17:15
  • $\begingroup$ What a great question !!!! $\endgroup$ – Fattie Feb 15 '18 at 21:31
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    $\begingroup$ For those inclined, paper 2601 from the 47th Lunar and Planetary Science Conference (2016) titled Ionizing Radiation on the Surface of Europa: Implications for the Search for Evidence of Life addresses this question using a Monte-Carlo simulation of realistic fluxes of the various components $\endgroup$ – uhoh Feb 16 '18 at 11:24
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Yes, it absolutely would! The radiation on Europa is about 5.4 Sv (540 rem) of radiation per day. Looking at this guide, and assuming you want to meet OSHA standards of 5 rem per year, you would need to only allow 1 part in 40,000 of the base radiation to make it through. The website linked indicates you want a mass of about 375 pounds/square foot to only allow 1 part in 1000. The chart says 72 inches of water. Ice isn't quite as dense, so a bit more ice. Let's say 2 m of ice will do. The factor is roughly $31^{\text{thickness}(m)}$, so to get the 40,000 value, you need about 3.1m. I would say leave an extra meter or two just to have a large buffer.

This has been further studied by a more scientific paper, if you would like to know more details.

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    $\begingroup$ Just out of curiosity, I wondered how thick that ice layer actually is, before you start to get into the ocean underneath? The answer seems to be "between 19 and 25 km" so there's plenty of material to work in! $\endgroup$ – KlaymenDK Feb 15 '18 at 14:25
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    $\begingroup$ And you really want to go a bit better than the OSHA standard here, for the standard is specifically for radiation workers. You don't want to expose ordinary colonists (including I presume children and pregnant women) for multiple decades to 5 rem a year. Luckily you got plenty of ice available, so I'd try to bring it down to 500 milirem a year whenever possible. $\endgroup$ – Mast Feb 15 '18 at 14:34
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    $\begingroup$ Suffice it to say... I think you're going to wind up with more ice above you for structural purposes than you are for radiation purposes. Convenient, honestly. $\endgroup$ – corsiKa Feb 15 '18 at 15:58
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    $\begingroup$ Relevant xkcd/what-if what-if.xkcd.com/29. "What if I took a swim in a typical spent nuclear fuel pool? Would I need to dive to actually experience a fatal amount of radiation? How long could I stay safely at the surface?" $\endgroup$ – csiz Feb 15 '18 at 18:35
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    $\begingroup$ Dropping by to wonder if, after a few million years of previous irradiance, the upper layers of ice might be somewhat radioactive themselves. Granted, H and O don't have many nasty byproducts, but I'd like to see the estimates. $\endgroup$ – Carl Witthoft Feb 15 '18 at 19:17

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