In the following list of equivalence classes, find two classes which are equal

Question

Consider the equivalence relation n $\Bbb R$ - {$0$}:

$a$~$b$ if and only if $\dfrac {a}{b} \in \Bbb Q $

In the following list of equivalence classes, find two classes which are equal:

[$\sqrt 3$] , [$1$], [$\sqrt {12}$], [$\sqrt 6$]

I have no idea how to do this question. Please prove the answer and explanations as this question could be on my test.

$[x]=[y]$ if and only if $x\sim y$, which is the case if and only if $\frac{x}y$ is rational. Find two numbers in the set ${\sqrt3,1,\sqrt{12},\sqrt6}$ whose ratio is rational. — Brian M. Scott, Dec 13 '13 at 01:07
Looks good to me: the ratio is $2$ or $\frac12$, depending on which way you take it, and that’s certainly rational. — Brian M. Scott, Dec 13 '13 at 01:16

score 1 · Answer 1 · answered Dec 13 '13 at 01:16

1

Think [$\sqrt12$] can be expressed as $2\sqrt3$ right? And you have a [$\sqrt3$]...

answered Dec 13 '13 at 01:16

Mac

1 Answers1