6.5³ + 20.5² - 25.5

asked by guest
on Jan 26, 2025 at 1:49 pm



You asked:

Evaluate the expression: \({6.5}^{3} + {20.5}^{2} - 25.5\)

MathBot Answer:

\[{6.5}^{3} + {20.5}^{2} - 25.5 = \frac{5355}{8} = 669.375\]

\[\begin{aligned}{6.5}^{3} + {20.5}^{2} - 25.5& = \left(6 + \frac{5}{10}\right)^{3} + \left(20 + \frac{5}{10}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \left(6 + \frac{1}{2}\right)^{3} + \left(20 + \frac{5}{10}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \left(\frac{13}{2}\right)^{3} + \left(20 + \frac{5}{10}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \frac{2197}{8} + \left(20 + \frac{5}{10}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \frac{2197}{8} + \left(20 + \frac{1}{2}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \frac{2197}{8} + \left(\frac{41}{2}\right)^{2} - \left(25 + \frac{5}{10}\right)\\& = \frac{2197}{8} + \frac{1681}{4} - \left(25 + \frac{5}{10}\right)\\& = \frac{2197}{8} + \frac{1681}{4} - \left(25 + \frac{1}{2}\right)\\& = \frac{2197}{8} + \frac{1681}{4} - \frac{51}{2}\\& = \frac{5559}{8} - \frac{51}{2}\\& = \frac{5355}{8}\end{aligned}\]

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