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обчисліть -5 3√64 - 6 5√-32+4√81

The expression \( -5 \cdot \sqrt[3]{64} - 6 \cdot \sqrt[5]{-32} + \sqrt[4]{81} \) evaluates to approximately \( -26.71 - 7.05i \), where \( i \) is the imaginary unit.

This indicates that the fifth root of \(-32\) introduces a complex number component. If you'd like, I can walk you through each step of the calculation or explain the complex number aspect in detail.

Would you like more details on this solution or an explanation on any part of the process?

Here are 5 related questions to explore further:
1. What are complex numbers and how do they arise in mathematical problems?
2. How do cube roots and other roots behave with negative numbers?
3. Can you simplify expressions involving radicals with complex numbers?
4. How do higher-order roots (like fifth or fourth roots) behave differently from square roots?
5. What are some applications of complex numbers in real-world problems?

**Tip:** When calculating roots of negative numbers, odd roots (e.g., cube roots) of negative values are real, but even roots (like square roots) introduce imaginary components.

Обчисліть -5 ∛64 - 6 ⁵√-32 + ⁴√81

Explore the detailed solution to the mathematical expression -5 ∛64 - 6 ⁵√-32 + ⁴√81, involving roots, complex numbers, and arithmetic operations. Learn how the fifth root of -32 introduces a complex number component and how to handle similar expressions. Suitable for students in Grades 10-12.

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