## Intermediate Algebra (12th Edition)

$p=9$
$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $\sqrt[3]{p+5}=\sqrt[3]{2p-4} ,$ raise both sides of the equation to the third power. Then use properties of equality to isolate and solve the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Raising both sides of the equation to the third power results to \begin{array}{l}\require{cancel} \left(\sqrt[3]{p+5}\right)^3=\left(\sqrt[3]{2p-4}\right)^3 \\\\ p+5=2p-4 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} p-2p=-4-5 \\\\ -p=-9 \\\\ p=9 .\end{array} Upon checking, $p=9$ satisfies the original equation.