Math Problem Statement
Diego says that if you cube the number 4 and then take the cube root of the result, you end up with 8. Is Diego correct?
Solution
Diego is incorrect.
Let's break down the process:
-
Cubing the number 4:
. -
Taking the cube root of the result:
.
So, the final result is 4, not 8.
If you cube 4 and then take the cube root, you should return to 4, not 8. Therefore, Diego's statement is incorrect.
Would you like further details or have any questions?
Here are 5 related questions:
- What happens when you take the square root of a squared number?
- How do cube roots work for negative numbers?
- Can you generalize this to other numbers like 5 or 6?
- What would happen if you cube and then take the fourth root of a number?
- What is the difference between square roots and cube roots in terms of function behavior?
Tip: Cube roots undo cubing, so they always return the original number when cubing and then taking the cube root!
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Math Problem Analysis
Mathematical Concepts
Exponentiation
Roots
Cube and Cube Root
Formulas
Cubing a number: x^3
Cube root of a number: ∛x
Theorems
The cube root undoes cubing for any real number
Suitable Grade Level
Grades 6-8