Math Problem Statement

Simplify the expression: ∛(3x) + 9∛(3x) − 2∛(3x).

Solution

The expression you uploaded is:

[ \sqrt[3]{3x} + 9 \sqrt[3]{3x} - 2 \sqrt[3]{3x} ]

Since all the terms contain the same cube root factor 3x3\sqrt[3]{3x}, they can be combined like like terms:

[ (1 + 9 - 2) \cdot \sqrt[3]{3x} = 8 \cdot \sqrt[3]{3x} ]

Thus, the simplified expression is:

83x38 \sqrt[3]{3x}

Would you like further details or have any questions about the simplification process?

Here are 5 related questions to deepen understanding:

  1. How would you simplify if the radicals were square roots instead of cube roots?
  2. What if the terms inside the radicals were different, say 4x3\sqrt[3]{4x} and 5x3\sqrt[3]{5x}?
  3. Can you explain how to distribute or combine cube roots in general?
  4. How do cube roots relate to exponents and how can you convert them to fractional exponents?
  5. How would the solution change if there were an additional term like 33x233 \sqrt[3]{3x^2}?

Tip: Always ensure that terms can be combined by checking if the radical expressions are identical before simplifying.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radicals
Cube Roots

Formulas

(a + b + c) ∛(n) = (a + b + c) × ∛(n)

Theorems

Like Terms with Radicals

Suitable Grade Level

Grades 8-10