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:

  1. Cubing the number 4:
    43=4×4×4=644^3 = 4 \times 4 \times 4 = 64.

  2. Taking the cube root of the result:
    643=4\sqrt[3]{64} = 4.

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:

  1. What happens when you take the square root of a squared number?
  2. How do cube roots work for negative numbers?
  3. Can you generalize this to other numbers like 5 or 6?
  4. What would happen if you cube and then take the fourth root of a number?
  5. 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