√0.144×0.96÷0.72×0.012

asked by guest
on Jan 22, 2025 at 9:09 am



You asked:

Evaluate the expression: 0.144⋅0.960.72⋅0.012\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012

MathBot Answer:

0.144⋅0.960.72⋅0.012=6103125≈0.00607157310752328831743787560531\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012 = \frac{6 \sqrt{10}}{3125} \approx 0.00607157310752328831743787560531

0.144⋅0.960.72⋅0.012=1441000⋅96100⋅172100⋅121000=18125⋅96100⋅172100⋅121000=325⋅10⋅96100⋅172100⋅121000=325⋅10⋅96100⋅11825⋅121000=325⋅10⋅96100⋅2518⋅121000=28825⋅10⋅1100⋅2518⋅121000=72625⋅10⋅2518⋅121000=425⋅10⋅121000=4825⋅10⋅11000=63125⋅10\begin{aligned}\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012&=\sqrt{\frac{144}{1000}} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\&=\sqrt{\frac{18}{125}} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\&=\frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\&=\frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{1}{\frac{18}{25}} \cdot \frac{12}{1000}\\&=\frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\&=\frac{288}{25} \cdot \sqrt{10} \cdot \frac{1}{100} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\&=\frac{72}{625} \cdot \sqrt{10} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\&=\frac{4}{25} \cdot \sqrt{10} \cdot \frac{12}{1000}\\&=\frac{48}{25} \cdot \sqrt{10} \cdot \frac{1}{1000}\\&=\frac{6}{3125} \cdot \sqrt{10}\end{aligned}

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