Solve the Inequality $10 < x ^ { 3 } - 1 < 32$

Multiple Choice

Solve the inequality $10 < x ^ { 3 } - 1 < 32$ . Restrict your attention to positive values of $x$ .

A) $\quad 3.37 < x < 3.21$
B) $\quad 2.22 < x < 3.21$
C) $\quad 2.22 < x < 8.19$
D) $3.37 < x < 8.19$ $$\sqrt { x } + \sqrt { x + 1 } > x + 1$$