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.

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- Apr 17th 2008, 06:51 PMBradley55Just 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 PMIsomorphism
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 PMBradley55
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 PMmr fantastic
Q is the symbol for rational numbers.

E is the symbol for "is an element of".

All Isomorphism is saying with this notation is that 0 and 4 are rational numbers ......

Isomorphism has given you a couple of examples of values of a and b that clearly and convincingly show the answer to both questions is yes.

(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 ......)