The particular risk of radioactive iodine is in children where it can be held by the body in the thyroid. Hence iodine supplements for kids when radioactive iodine is significant.
Just because something can be detected doesn't mean its harmful in the quantities detected.
ETA: The other thing with radioactive iodine is that its half-life is 8 days, so what was detected in March would be basically gone by April.
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Uncertainty is an uncomfortable position.
But certainty is an absurd one.
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