3∛250+4∛192−2∛24−∛128

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



You asked:

Evaluate the expression: 32503+41923−2243−12833 \sqrt[3]{250} + 4 \sqrt[3]{192} - 2 \sqrt[3]{24} - \sqrt[3]{128}

MathBot Answer:

32503+41923−2243−1283=11⋅23+12⋅33≈31.166126392532505400298976409421833 \sqrt[3]{250} + 4 \sqrt[3]{192} - 2 \sqrt[3]{24} - \sqrt[3]{128} = 11 \cdot \sqrt[3]{2} + 12 \cdot \sqrt[3]{3} \approx 31.16612639253250540029897640942183

32503+41923−2243−1283=3⋅2503+4⋅1923−2⋅243−1283=3⋅5⋅23+4⋅1923−2⋅243−1283=15⋅23+4⋅1923−2⋅243−1283=15⋅23+4⋅4⋅33−2⋅243−1283=15⋅23+16⋅33−2⋅243−1283=15⋅23+16⋅33−2⋅2⋅33−1283=15⋅23+16⋅33−4⋅33−1283=15⋅23+16⋅33−4⋅33−4⋅23=(15⋅23+16⋅33)−4⋅33−4⋅23=(12⋅33+15⋅23)−4⋅23=11⋅23+12⋅33\begin{aligned}3 \sqrt[3]{250} + 4 \sqrt[3]{192} - 2 \sqrt[3]{24} - \sqrt[3]{128}&=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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