Question 752418
Between 2 and 3 there are infinite irrational numbers (and infinite rational numbers too).
 
ONE IDEA:
If {{{sqrt(x)}}} is between 2 and 3,
then {{{2<sqrt(x)<3}}} means that {{{2^2<(sqrt(x))^2<3^2}}}, which means {{{4<x<9}}}
So {{{highlight(sqrt(5))}}} is a solution, and so are
{{{highlight(sqrt(6))}}} , {{{highlight(sqrt(7))}}}, and {{{highlight(sqrt(8))}}}.
 
FANCIER IDEAS:
You probably know that {{{pi}}} is an irrational number that is between 3 and 4.
So {{{3<pi<4}}} means that {{{2=3-1<pi-1<4-1<3}}}.
{{{highlight( pi-1 )}}} is another irrational number between 2 and 3.
 
FANCIER:
You may not know it, but there is an irrational number called {{{e}}} that is approximately 2.7183.
It is sort of like {{{pi}}} in that there is no other way to express it, and to describe it you have to tell a story. However, the story of {{{e}}} is more complicated than the story of {{{pi}}}.