How long does it take for only one eighth of a sample of radon-222 to remain

1/8 = (1/2) ^3 and the half life of radon is 3.8days

Half life is the time it takes for half of any amount of a radioactive substance to decay into something else.

Therefore for a sample of radon to decay to 1/8 of its original amount, it would take 3 x 3.8days=11.4 days