# Just a another one of those problems :)

• Apr 17th 2008, 06:51 PM
Just a another one of those problems :)
Hey guys im glad i found this site!

With a and b as irrationals, is it possible for their sum or difference to be rational? Give a convincing argument for your response.

Is it possible for a^b to be rational? Give a convincing argument.
• Apr 17th 2008, 07:00 PM
Isomorphism
Hey guys im glad i found this site!

With a and b as irrationals, is it possible for their sum or difference to be rational? Give a convincing argument for your response.
$\displaystyle \color{red} \sqrt{2} + {(-\sqrt{2})} = 0 \in \mathbb{Q}$
$\displaystyle \color{red}\sqrt{2} - {\sqrt{2}} = 0 \in \mathbb{Q}$

Is it possible for a^b to be rational? Give a convincing argument.

$\displaystyle \color{red}(2^{\sqrt{2}})^{\sqrt{2}} = 4 \in \mathbb{Q}$
• Apr 17th 2008, 07:27 PM
Im not sure my teacher would let me right E Q in my anwser because i have no idea what that means
• Apr 17th 2008, 08:31 PM
mr fantastic
Quote:

(For the second part, "Is it possible for a^b to be rational", if your teacher wants you to prove that $\displaystyle a = 2^{\sqrt{2}}$ is irrational, just smirk and refer him/her to the Gelfond-Schneider Theorem ......)