3∛250+4∛192−2∛24−∛128

asked by guest
on Nov 28, 2024 at 7:46 am



You asked:

Evaluate the expression: \(3 \cdot \sqrt[3]{250} + 4 \cdot \sqrt[3]{192} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}\)

MathBot Answer:

\[3 \cdot \sqrt[3]{250} + 4 \cdot \sqrt[3]{192} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128} = 11 \cdot \sqrt[3]{2} + 12 \cdot \sqrt[3]{3} \approx 31.16612639253250540029897640942183\]

\[\begin{aligned}3 \cdot \sqrt[3]{250} + 4 \cdot \sqrt[3]{192} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}& = 3 \cdot 5 \cdot \sqrt[3]{2} + 4 \cdot \sqrt[3]{192} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 4 \cdot \sqrt[3]{192} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 4 \cdot 4 \cdot \sqrt[3]{3} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 16 \cdot \sqrt[3]{3} - 2 \cdot \sqrt[3]{24} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 16 \cdot \sqrt[3]{3} - 2 \cdot 2 \cdot \sqrt[3]{3} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 16 \cdot \sqrt[3]{3} - 4 \cdot \sqrt[3]{3} - \sqrt[3]{128}\\& = 15 \cdot \sqrt[3]{2} + 16 \cdot \sqrt[3]{3} - 4 \cdot \sqrt[3]{3} - 4 \cdot \sqrt[3]{2}\\& = \left(15 \cdot \sqrt[3]{2} + 16 \cdot \sqrt[3]{3}\right) - 4 \cdot \sqrt[3]{3} - 4 \cdot \sqrt[3]{2}\\& = \left(12 \cdot \sqrt[3]{3} + 15 \cdot \sqrt[3]{2}\right) - 4 \cdot \sqrt[3]{2}\\& = 11 \cdot \sqrt[3]{2} + 12 \cdot \sqrt[3]{3}\end{aligned}\]

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