a square root of an irrational number

Question

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).

The square of a rational number is rational, so the square root of an irrational number must be irrational. — Daniel Fischer, Sep 20 '13 at 18:29

score 3 · Accepted Answer · answered Sep 20 '13 at 18:29

3

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.

answered Sep 20 '13 at 18:29

Matt Rigby

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a square root of an irrational number

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