Chapter 9 - Roots and Radicals - 9.5 - Solving Radical Equations - Problem Set 9.5 - Page 425: 51

{$57$}

Step 1: $\sqrt[3] {x+7}=4$ Step 2: Raising each side of the equation to the power of $3$ and simplifying, we find: $(\sqrt[3] {x+7})^{3}=(4)^{3}$ $x+7=64$ Step 3: Solving the equation, we obtain: $x+7=64$ $x=64-7$ $x=57$ Therefore, the solution set of the equation is {$57$}.