# Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 668: 35

$y=-\dfrac{5}{3}$

#### Work Step by Step

Using the properties of equality, the given equation, $\sqrt[3]{3y+6}+7=8$, is equivalent to \begin{array}{l} \sqrt[3]{3y+6}=8-7 \\\\ \sqrt[3]{3y+6}=1 .\end{array} Raising both sides to the $\text{ 3rd }$ power, the solution to the equation above, $\sqrt[3]{3y+6}=1$, is \begin{array}{l} 3y+6=1 \\\\ 3y=1-6 \\\\ 3y=-5 \\\\ y=-\dfrac{5}{3} .\end{array}

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