Answer
$x$ $\approx$ $-2.52$
Work Step by Step
Given equation is-
$x^{3}+16$ = $0$
Algebraic Solution:
$x^{3}$ = $-16$
i.e. $x^{3}$ = $(-4\sqrt 2)^{2}$
i.e. $x$ = $\sqrt[3] {-16}$
i.e. $x$ = $-2.5198420998$
i.e. $x$ $\approx$ $-2.52$
Graphical Solution:
$x^{3}+16$ = $0$
Now graphing $y$ = $x^{3}+16$
$x-intercepts$ is $-2.5198$
i.e. $x$ = $-2.5198$
i.e. $x$ $\approx$ $-2.52$