6.5³ + 4.5³ - 5³

asked by guest
on Jan 26, 2025 at 1:52 pm



You asked:

Evaluate the expression: \({6.5}^{3} + {4.5}^{3} - {5}^{3}\)

MathBot Answer:

\[{6.5}^{3} + {4.5}^{3} - {5}^{3} = \frac{963}{4} = 240.75\]

\[\begin{aligned}{6.5}^{3} + {4.5}^{3} - {5}^{3}& = \left(6 + \frac{5}{10}\right)^{3} + \left(4 + \frac{5}{10}\right)^{3} - 5^{3}\\& = \left(6 + \frac{1}{2}\right)^{3} + \left(4 + \frac{5}{10}\right)^{3} - 5^{3}\\& = \left(\frac{13}{2}\right)^{3} + \left(4 + \frac{5}{10}\right)^{3} - 5^{3}\\& = \frac{2197}{8} + \left(4 + \frac{5}{10}\right)^{3} - 5^{3}\\& = \frac{2197}{8} + \left(4 + \frac{1}{2}\right)^{3} - 5^{3}\\& = \frac{2197}{8} + \left(\frac{9}{2}\right)^{3} - 5^{3}\\& = \frac{2197}{8} + \frac{729}{8} - 5^{3}\\& = \frac{2197}{8} + \frac{729}{8} - 125\\& = \frac{1463}{4} - 125\\& = \frac{963}{4}\end{aligned}\]

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