ex1.6_15

$y$ $\quad (y+8)^3-16=0$

$16$ to both sides to get

(y+8)^3=16.

Now that the cubic expression is on the left-hand side by itself, we simply take a cube root of both sides and solve.

(y+8)^3=16\\[0.25 in] y+8 = \sqrt[3]{16}\\[0.25 in] y = \sqrt[3]{16} - 8\\[0.25 in]

This answer can be simplified by simplifying the radical. Since

\sqrt[3]{16} = \sqrt[3]{8} \, \sqrt[3]{2} = 2 \, \sqrt[3]{2},

it follows that our final answer is

y=2 \, \sqrt[3]{2}-8 \quad \mbox{or} \quad y \approx -5.480.