Question

cubic and cube root functions and equations
which statement describes how to solve $sqrt3{x^2 - 6} = sqrt3{2x + 2}$?
square both sides and then solve the resulting cubic equation.
cube both sides and then solve the resulting quadratic equation.
cube both sides and then solve the resulting cubic equation.
square both sides and then solve the resulting quadratic equation.

Explanation:

To eliminate cube roots, we use the property that if $\sqrt[3]{A} = \sqrt[3]{B}$, then cubing both sides gives $A = B$. Cubing $\sqrt[3]{x^2 - 6}$ and $\sqrt[3]{2x + 2}$ will remove the cube roots, resulting in a quadratic equation ($x^2 - 6 = 2x + 2$) which can then be solved.

Answer:

Cube both sides and then solve the resulting quadratic equation.