((8\sqrt(7)-7)+(9\sqrt(7)-9))/(2)*(\sqrt(7+2))

asked by guest
on Sep 19, 2024 at 9:44 am



You asked:

Evaluate the expression: \(\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \sqrt{7 + 2}\)

MathBot Answer:

\[\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \sqrt{7 + 2} = -24 + \frac{51 \sqrt{7}}{2} \approx 43.46665843214706005779120171780114\]

\[\begin{aligned}\frac{8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9}{2} \cdot \sqrt{7 + 2}& = \left(8 \cdot \sqrt{7} - 7 + 9 \cdot \sqrt{7} - 9\right) \cdot \frac{1}{2} \cdot \sqrt{7 + 2}\\& = \left(\left(-7 + 8 \cdot \sqrt{7}\right) + 9 \cdot \sqrt{7} - 9\right) \cdot \frac{1}{2} \cdot \sqrt{7 + 2}\\& = \left(\left(-7 + 17 \cdot \sqrt{7}\right) - 9\right) \cdot \frac{1}{2} \cdot \sqrt{7 + 2}\\& = \left(-16 + 17 \cdot \sqrt{7}\right) \cdot \frac{1}{2} \cdot \sqrt{7 + 2}\\& = \left(-16 + 17 \cdot \sqrt{7}\right) \cdot \frac{1}{2} \cdot \sqrt{9}\\& = \left(-16 + 17 \cdot \sqrt{7}\right) \cdot \frac{3}{2}\\& = \left(-8 + \frac{17}{2} \cdot \sqrt{7}\right) \cdot 3\\& = -24 + \frac{51}{2} \cdot \sqrt{7}\end{aligned}\]

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