We prove if a sequence of nonnegative numbers converges to a limit, then the square root of that sequence converges to the square root of that limit, which we could call the square root limit law or limit law for square roots. #RealAnalysis
Put more precisely, if every x_n is at least 0, and the sequence (x_n) converges to x, then the sequence of square roots (sqrt(x_n)) converges to sqrt(x). Note that each x_n needs to be at least 0 since we are taking square root of x_n. We don't need to require the limit x be at least 0 because it is impossible for a nonnegative sequence like (x_n) to have a negative limit. So x is certainly at least 0.
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Nonnegative Convergent Sequence has Nonnegative Limit: (coming soon)
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