# Thread: Just a another one of those problems :)

1. ## 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.

2. 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.
$\color{red} \sqrt{2} + {(-\sqrt{2})} = 0 \in \mathbb{Q}$
$\color{red}\sqrt{2} - {\sqrt{2}} = 0 \in \mathbb{Q}$

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

$\color{red}(2^{\sqrt{2}})^{\sqrt{2}} = 4 \in \mathbb{Q}$

3. Im not sure my teacher would let me right E Q in my anwser because i have no idea what that means

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