Question

solve ( v^{3} = -29 ) where ( v ) is a real number. simplify your answer as much as possible. (if there is more than one solution, separate them with commas.) ( v = )

Explanation:

Step1: Take cube root of both sides

To isolate \(v\), apply the cube root to each side of the equation.
$$\sqrt[3]{v^3} = \sqrt[3]{-29}$$

Step2: Simplify both sides

The cube root of \(v^3\) is \(v\), and \(\sqrt[3]{-29}\) can be rewritten as \(-\sqrt[3]{29}\) since the cube root of a negative number is negative.
$$v = -\sqrt[3]{29}$$

Answer:

\(v = -\sqrt[3]{29}\)