I wonder if a square root of an irrational number is always irrational?
I would tend to think that yes, but I can´t think of any justification. Also there are cases which are rather hard to decide like sqrt(Pi).
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Sign up to join this communityI wonder if a square root of an irrational number is always irrational?
I would tend to think that yes, but I can´t think of any justification. Also there are cases which are rather hard to decide like sqrt(Pi).
Yes. The square of a rational is rational, so the identity $x = (\sqrt{x})^2$ tells us that if the square root is rational, the original number must be too.