Question

solve ( v^3 = -25 ) where ( v ) is a real number. simplify your answer as much as possible. (if there is more than one solution, separate them with commas.)

Explanation:

Step1: Take cube root of both sides

To isolate \(v\), apply cube root to each side of the equation.
$$\sqrt[3]{v^3} = \sqrt[3]{-25}$$

Step2: Simplify both sides

The cube root of \(v^3\) is \(v\), and \(\sqrt[3]{-25}\) can be rewritten as \(-\sqrt[3]{25}\) (since cube roots preserve negative signs for real numbers).
$$v = -\sqrt[3]{25}$$

Answer:

\(v = -\sqrt[3]{25}\)