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From: Earle Jones on 20 Jul 2010 00:57
In article
<d0a5b861-32e4-4a3a-9a3c-a20eab19b06e(a)v37g2000vbv.googlegroups.com>,
Craig Feinstein <cafeinst(a)msn.com> wrote:

> Is the following possible?
>
> a,b are irrational. c is rational. ab=c^2.
>
> Why or why not?
>
> Craig

*
a = pi
b = 1/pi

a,b irrational

ab = 1

c = 1

ab = c^2

QED.

earle
*
From: Virgil on 20 Jul 2010 02:35
In article
<d0a5b861-32e4-4a3a-9a3c-a20eab19b06e(a)v37g2000vbv.googlegroups.com>,
Craig Feinstein <cafeinst(a)msn.com> wrote:

> Is the following possible?
>
> a,b are irrational. c is rational. ab=c^2.
>
> Why or why not?
>
> Craig

a = sqrt(2) - 1 is irrational,
b = sqrt(2) + 1 is irrational,
c = 1 is rational
and a*b = c^2.
From: Ludovicus on 20 Jul 2010 08:47
On 1 jun, 12:19, Craig Feinstein <cafei...(a)msn.com> wrote:
> Is the following possible?
> a,b are irrational. c is rational. ab=c^2.
> Why or why not?
> Craig

A true platitude.
If a and b are irrational only if a.b is a perfect square
can a.b = c^2
Example a = sqr(2) ; b = sqr(32) ; c = 8

From: Alois Steindl on 20 Jul 2010 09:06
Ludovicus <luiroto(a)yahoo.com> writes:

> On 1 jun, 12:19, Craig Feinstein <cafei...(a)msn.com> wrote:
>> Is the following possible?
>> a,b are irrational. c is rational. ab=c^2.
>> Why or why not?
>> Craig
>
> A true platitude.
> If a and b are irrational only if a.b is a perfect square
> can a.b = c^2
> Example a = sqr(2) ; b = sqr(32) ; c = 8
Hello,
first 2 remarks:
sqr(x) is often used for "square" of x = x^2, the square root is written
as sqrt(x).
In your example a*b=c, not a*b=c^2.

But one could take say c=8 (any nonzero rational number would work) and
a=c*r, b=c/r, where r is any irrational number, like sqrt(2), or pi or
anything else.

Alois

From: Virgil on 20 Jul 2010 15:55
In article
<3201a1e3-9f91-45cc-81d6-69144da9a5d6(a)k19g2000yqc.googlegroups.com>,
Ludovicus <luiroto(a)yahoo.com> wrote:

> On 1 jun, 12:19, Craig Feinstein <cafei...(a)msn.com> wrote:
> > Is the following possible?
> > a,b are irrational. c is rational. ab=c^2.
> > Why or why not?
> > Craig
>
> A true platitude.
> If a and b are irrational only if a.b is a perfect square
> can a.b = c^2
> Example a = sqr(2) ; b = sqr(32) ; c = 8

For your "example", a.b = c, not a.b = c^2

Try a = sqrt(2), b = sqrt(8), c = 2
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