# Proof that any fractional number squared is also fractional? [duplicate]

Let a belong to the set of (Rationals - Integers)

How would you prove the following:

a squared belongs to the set of (Rationals - Integers)

## marked as duplicate by Matthew Conroy, dxiv, CIJ, Bill Dubuque number-theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 30 '17 at 22:59

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• The body of the question doesn't match the title. Which one are you asking? In case it matters, remember that $\,i^2=-1\,$, and $\big(\sqrt{2}\big)^2=2$. – dxiv Aug 30 '17 at 22:42
• Sorry I meant set of Complex minus set of Integers – user448724 Aug 30 '17 at 22:43
• $i^2=-1$ your statement is false. – hamam_Abdallah Aug 30 '17 at 22:46
• Ah yes of course. I'm going to update the question to be irrational set minus integer. – user448724 Aug 30 '17 at 22:49
• If the dupes don't answer your question then please clarify why and we can reopen the question. – Bill Dubuque Aug 30 '17 at 23:01