Question

what is the solution of \\(\sqrt3{x + 8} = -4\\)?
\\(x = -72\\)
\\(x = -66\\)
\\(x = 58\\)
no solution

Explanation:

Step1: Cube both sides of the equation

To solve the equation \(\sqrt[3]{x + 8}=-4\), we cube both sides. Cubing the left side gives us \(x + 8\) (since \((\sqrt[3]{a})^3=a\)), and cubing the right side gives us \((-4)^3=-64\). So we have the equation \(x + 8=-64\).

Step2: Solve for \(x\)

Subtract 8 from both sides of the equation \(x + 8=-64\). That is \(x=-64 - 8\). Calculating the right side, we get \(x=-72\).

Answer:

\(x = - 72\) (the option with " \(x=-72\)")