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![\text{If is}\ 3\sqrt{x+8}=-4,\ \text{then the equation has no solution, because}\ \sqrt{a}\geq0.\\\\\text{If is}\ \sqrt[3]{x+8}=-4,\ \text{then:}\\\\\sqrt[3]{x+8}=-4\qquad\text{third power of both sides}\\\\(\sqrt[3]{x+8})^3=(-4)^3\qquad\text{use}\ (\sqrt[n]{a})^n=a\\\\x+8=-64\qquad\text{subtract 8 from both sides}\\\\\boxed{x=-72}](/tpl/images/0491/9691/6c6bb.png)
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