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From: Craig Feinstein on 1 Jun 2010 12:19
Is the following possible?

a,b are irrational. c is rational. ab=c^2.

Why or why not?

Craig
From: José Carlos Santos on 1 Jun 2010 12:24
On 01-06-2010 17:19, Craig Feinstein wrote:

> Is the following possible?
>
> a,b are irrational. c is rational. ab=c^2.

Sure. a = sqrt(2), b = 1/sqrt(2) and c = 1.

Best regards,

Jose Carlos Santos
From: Craig Feinstein on 1 Jun 2010 12:37
On Jun 1, 12:24 pm, José Carlos Santos <jcsan...(a)fc.up.pt> wrote:
> On 01-06-2010 17:19, Craig Feinstein wrote:
>
> > Is the following possible?
>
> > a,b are irrational. c is rational. ab=c^2.
>
> Sure. a = sqrt(2), b = 1/sqrt(2) and c = 1.
>
> Best regards,
>
> Jose Carlos Santos

Thank you, that was too simple. I really meant to ask is the following
possible?

a^2 and b^2 are irrational. c is rational. ab=c^2.

Craig
From: Mike Terry on 1 Jun 2010 12:45
"Craig Feinstein" <cafeinst(a)msn.com> wrote in message
news:bb2d0bb1-139b-4ada-b42a-f9d3077247b6(a)s41g2000vba.googlegroups.com...
> On Jun 1, 12:24 pm, Jos� Carlos Santos <jcsan...(a)fc.up.pt> wrote:
> > On 01-06-2010 17:19, Craig Feinstein wrote:
> >
> > > Is the following possible?
> >
> > > a,b are irrational. c is rational. ab=c^2.
> >
> > Sure. a = sqrt(2), b = 1/sqrt(2) and c = 1.
> >
> > Best regards,
> >
> > Jose Carlos Santos
>
> Thank you, that was too simple. I really meant to ask is the following
> possible?
>
> a^2 and b^2 are irrational. c is rational. ab=c^2.

Well, there was nothing very special about the number 2 in Jos�'s example -
e.g. replace the number 2 with an irrational number like Pi...

Mike.



From: William Hughes on 1 Jun 2010 12:45
On Jun 1, 1:37 pm, Craig Feinstein <cafei...(a)msn.com> wrote:
> On Jun 1, 12:24 pm, José Carlos Santos <jcsan...(a)fc.up.pt> wrote:
>
> > On 01-06-2010 17:19, Craig Feinstein wrote:
>
> > > Is the following possible?
>
> > > a,b are irrational. c is rational. ab=c^2.
>
> > Sure. a = sqrt(2), b = 1/sqrt(2) and c = 1.
>
> > Best regards,
>
> > Jose Carlos Santos
>
> Thank you, that was too simple. I really meant to ask is the following
> possible?
>
> a^2 and b^2 are irrational. c is rational. ab=c^2.
>
> Craig

Hint: sqrt(1) = 1

- William Hughes
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