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