How to check if a square root is irrational

Anonymous

What's the easiest way in sage to check if the square root of a given rational number (for example 1,671 or 2,56) is irrational.

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Convert your numbers to explicit rationals and ask whether their square root is in Q:

sage: sqrt(1671/1000) in QQ
False
sage: sqrt(256/100) in QQ
True
sage: sqrt(2) in QQ
False

Or you can do the conversions this way:

sage: sqrt(QQ(1.671)) in QQ
False

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Asked: 12 years ago

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Last updated: Oct 13 '12