I read the statement in the title somewhere but I can't find any proof.
For a positive integer $n$, why can't there be 4 numbers $a, b, c, d$ ($b$ and $d$ are prime) for which
$a < \sqrt{n} < b$, where $a \cdot b = n$
and
$c < \sqrt{n} < d$, where $c \cdot d = n$