7* 10∗10−6\sqrt{10*10-6} -(7*2*2*2+8)/3

asked by guest
on Mar 17, 2025 at 6:01 pm



You asked:

Evaluate the expression: 710⋅10−6−7⋅2⋅2⋅2+837 \sqrt{10 \cdot 10 - 6} - \frac{7 \cdot 2 \cdot 2 \cdot 2 + 8}{3}

MathBot Answer:

710⋅10−6−7⋅2⋅2⋅2+83=−643+794≈46.534184670495272863708834722583867 \sqrt{10 \cdot 10 - 6} - \frac{7 \cdot 2 \cdot 2 \cdot 2 + 8}{3} = - \frac{64}{3} + 7 \sqrt{94} \approx 46.53418467049527286370883472258386

710⋅10−6−7⋅2⋅2⋅2+83=7⋅10⋅10−6−(7⋅2⋅2⋅2+8)⋅13=7⋅100−6−(7⋅2⋅2⋅2+8)⋅13=7⋅94−(7⋅2⋅2⋅2+8)⋅13=7⋅94−(14⋅2⋅2+8)⋅13=7⋅94−(28⋅2+8)⋅13=7⋅94−(56+8)⋅13=7⋅94−643=−643+7⋅94\begin{aligned}7 \sqrt{10 \cdot 10 - 6} - \frac{7 \cdot 2 \cdot 2 \cdot 2 + 8}{3}&=7 \cdot \sqrt{10 \cdot 10 - 6} - \left(7 \cdot 2 \cdot 2 \cdot 2 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{100 - 6} - \left(7 \cdot 2 \cdot 2 \cdot 2 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{94} - \left(7 \cdot 2 \cdot 2 \cdot 2 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{94} - \left(14 \cdot 2 \cdot 2 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{94} - \left(28 \cdot 2 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{94} - \left(56 + 8\right) \cdot \frac{1}{3}\\&=7 \cdot \sqrt{94} - \frac{64}{3}\\&=- \frac{64}{3} + 7 \cdot \sqrt{94}\end{aligned}

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