Answer
$$\left( {1,\infty } \right)$$
Work Step by Step
$$\eqalign{
& x\sqrt {x - 1} > 0 \cr
& \sqrt {x - 1} {\text{ is always positive and }}x > 1 \cr
& {\text{Then}} \cr
& {\text{The solution of the inequality is }}\left( {1,\infty } \right) \cr} $$