Simplify the given expression. [tex]$\sqrt[3]{y^3}$[/tex]
Answer (1)
Recognize that the cube root and cubing operations are inverses of each other.
Apply the property 3 y 3 = y .
Simplify the expression to obtain the final answer.
The simplified expression is y .
Explanation
Understanding the Problem We are asked to simplify the expression 3 y 3 . This involves understanding the properties of radicals and exponents.
Applying the Property of Radicals The cube root of a number raised to the power of 3 is the number itself. Mathematically, 3 y 3 = y . This is because the cube root operation is the inverse of cubing a number.
Final Answer Therefore, the simplified expression is simply y .
Examples
Imagine you have a cube-shaped box, and you want to find the length of one of its sides. If you know the volume of the cube is y 3 , then taking the cube root, 3 y 3 , gives you the length of one side, which is y . This concept is useful in various fields like engineering and architecture when dealing with volumes and dimensions.
