How to undo a cube root?
Understand the Problem
The question is asking how to reverse or undo the operation of taking the cube root of a number. This involves understanding the mathematical relationship between cube roots and their inverses, which is raising a number to the power of three.
Answer
The inverse operation of taking the cube root is $x = y^3$.
Answer for screen readers
The inverse operation of taking the cube root is raising a number to the third power, represented mathematically as $x = y^3$.
Steps to Solve
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Identify the operation
The operation we want to reverse is the cube root, represented mathematically as $\sqrt[3]{x}$. -
Establish the inverse operation
To reverse the cube root, we need to raise the number back to the power of three. Mathematically, if $y = \sqrt[3]{x}$, then to undo this we can write: $$ x = y^3 $$ -
Solve for the original number
If we have a specific value for $y$, we can find $x$ by cubing that value. For example, if $y = 2$, we find: $$ x = 2^3 = 8 $$ -
Generalize the inverse operation
Therefore, we can say that the operation to reverse the cube root of a number can be summarized as: $$ x = y^3 $$
where $y$ is the result of the cube root operation.
The inverse operation of taking the cube root is raising a number to the third power, represented mathematically as $x = y^3$.
More Information
The cube root operation is quite common in various mathematical fields, including geometry and algebra. For instance, finding the side length of a cube when you know its volume involves taking the cube root, while going back to the volume requires cubing the side length.
Tips
- Confusing the cube root with taking the square root, leading to incorrect inverse operations. To avoid this, always remember that the cube root undoes the operation of cubing, not squaring.
