Math Problem Statement

X; x^3=64

Solution

To solve the equation x3=64x^3 = 64, we need to find the value of xx such that its cube equals 64.

Step-by-step solution:

  1. Start with the equation: x3=64x^3 = 64
  2. To solve for xx, take the cube root of both sides: x=643x = \sqrt[3]{64}
  3. Since 64=4364 = 4^3, the cube root of 64 is: x=4x = 4

Thus, x=4x = 4 is the solution.

Would you like a more detailed explanation or have any questions?

Here are some related questions to consider:

  1. How do you calculate cube roots for negative numbers?
  2. What is the general method for solving equations involving higher powers, like xnx^n?
  3. How do cube roots apply in real-world scenarios?
  4. Can equations like x3=64x^3 = 64 have multiple solutions in complex numbers?
  5. How does cube root differ from square root in terms of their geometric interpretations?

Tip: To check your solution, always substitute the value of xx back into the original equation to verify it works.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Cube Roots

Formulas

x^3 = a, x = ∛a

Theorems

Cube root properties

Suitable Grade Level

Grades 8-10