# Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 41

$m=14$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $\sqrt[3]{2m-1}=\sqrt[3]{m+13} ,$ 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]{2m-1} \right)^3=\left( \sqrt[3]{m+13} \right)^3 \\\\ 2m-1=m+13 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2m-m=13+1 \\\\ m=14 .\end{array} Upon checking, $m=14$ satisfies the original equation.

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