S＜２

$ rad(abc)^2\gt{}c$
$rad(ab)\cdot{}d\gt\sqrt{c}$
$\sqrt{c}\cdot{}rad(ab)\cdot{}d\gt{}c$
$rad(ab)\cdot\sqrt{c}\gt\frac{c}{d}$
$\sqrt{c}\cdot{}rad(ab)\cdot{}d\gt\sqrt{c}$
$rad(ab)\cdot\sqrt{c}\gt\sqrt{c}\leqq\frac{c}{2}$
$rad(ab)\cdot\sqrt{c}\gt\frac{c}{d}\leqq\frac{c}{2}$
$\sqrt{c}\cdot{}rad(abc)\gt\frac{c}{d}\cdot{}rad(c)$
$\sqrt{c}\cdot{}rad(abc)\cdot\frac{d}{rad(c)}\gt{}c$
$d\longrightarrow{}rad(c)$
$\sqrt{c}\cdot{}rad(ab)\cdot{}d\gt\sqrt{c}$
$\sqrt{c}\cdot{}rad(ab)\cdot{}d\gt{}c$
$rad(ab)\cdot\sqrt{c}\gt\frac{c}{d}$
$rad(ab)\cdot{}d\gt\sqrt{c}$
$rad(abc)^2\gt{}c$

$rad(abc)^S=c$
$S\lt{2}$