Answer
$4$ $kg/m$
Work Step by Step
The linear density $ρ$ is the rate of change of mass $m$ with respect to length $x$
$m$ = $x(1+\sqrt x)$ = $x+x^{\frac{3}{2}}$
$ρ$ = $\frac{dm}{dx}$ = $1+\frac{3}{2}\sqrt x$
so the linear density when $x$ = $4$ is
$1+\frac{3}{2}\sqrt 4$ = $4$ $kg/m$
