Square root of an odd composite being irrational

Question

Is there an odd composite number $n$ such that $\sqrt{n}$ is irrational?

Any $n$ that isn't a perfect square. Lots of odd composite numbers aren't perfect squares, as @MJD's comment suggests. — , Jun 11 '14 at 18:30

score 5 · Accepted Answer · answered Jun 11 '14 at 15:31

5

HINT:

The sufficient condition for $\sqrt n$ is irrational is $n$ be not perfect square i.e., at least one prime factor of $n$ has odd power

answered Jun 11 '14 at 15:31

lab bhattacharjee

It is also necessary. – lhf Jun 11 '14 at 16:00
@lhf, I Was thinking about $$\sqrt e,\sqrt \pi$$ – lab bhattacharjee Jun 11 '14 at 16:01
But $n$ is an integer here, right? – lhf Jun 11 '14 at 16:02
@lhf, I was trying to generalize – lab bhattacharjee Jun 11 '14 at 16:04

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