Question

solve ( w^3 = 22 ) where ( w ) is a real number. simplify your answer as much as possible. (if there is more than one solution, separate them with commas.) ( w = square )

Explanation:

Step1: Take cube root of both sides

To solve for \( w \) in the equation \( w^3 = 22 \), we take the cube root of both sides. The cube root of a number \( x \) is denoted as \( \sqrt[3]{x} \), and for the equation \( w^3 = 22 \), applying the cube root to both sides gives \( w=\sqrt[3]{22} \). Since we are dealing with real numbers, and every real number has exactly one real cube root, this is the only solution.

Answer:

\( \sqrt[3]{22} \)