Wikipedia:Reference desk/Archives/Mathematics/2008 September 6#heights and distance

I would like to have a brief information on this topic'heights and distance' as i have to use the information as my class 10th board examination 2008 project —Preceding unsigned comment added by 117.197.48.170 (talk) 15:15, 6 September 2008 (UTC)

:Can you be more specific? It is impossible to be brief in response to such a general question. Wikiant (talk) 16:56, 6 September 2008 (UTC)

::Is trajectory of interest?…86.132.239.22 (talk) 17:45, 6 September 2008 (UTC)

:Which board? Also, try height and distance. – b_jonas 20:26, 6 September 2008 (UTC)

117.197.48.170: This is an experiment. If you see this then just let us know somehow. Thanks, -hydnjo talk 23:27, 6 September 2008 (UTC)

:Please use WP:SANDBOX for your experiments.Cuddlyable3 (talk) 09:28, 9 September 2008 (UTC)

If a and b are positive integers and not both square, is it possible for sqrt(a)+sqrt(b) to be rational? Black Carrot (talk) 22:02, 6 September 2008 (UTC)

:No. Algebraist 22:08, 6 September 2008 (UTC)

::Let d be the HCF of a and b. Then we have sqrt(d)(sqrt(a')+sqrt(b')) rational, with a' and b' coprime. Squaring we find that sqrt(a'b') is rational, so a' and b' are both squares. But then sqrt(d) is rational, so d is a square, so a and b are both squares after all. Algebraist 22:11, 6 September 2008 (UTC)