No. First the united states wouldn't want to start an international fiasco that would certainly come out of it, especially since china would not tolerate such a thing. Plus you have the fact that the general belief held among world governments is to free the people of north korea, not boil their skin off and poison and make their land uninhabitable for the next century.
There would be a major shitstorm and likely an invasion, but no nukes.
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I don't think it would inhabitable for the next century, Hiroshima was able to be walked through not long after, and Chernobyl is returning to normal level, with most of the radiation being inside buildings.
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Modern nukes are significantly more powerful than hiroshima and chernobyl combined, though even then that was just a secondary concern after the whole international shitstorm that nuking North Korea would start.
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That is an excellent point.
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Well, you can always use clean bombs essentially relying almost entirely on fusion. wiping out life and having the radiation gone in a few weeks too months, these are basically used to kill all organic life in a certain radius while keeping buildings and other structures alive for the invading force. Or you could use Pure Fusion weapons, but those are not done being tested fully yet.
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That sounds awesome, you think NK has any oil over there? Or anything of value?
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Well they do have resources, no doubt about it. But they don't actually have enough of anything worth while for us to really take.