√0.144×0.96÷0.72×0.012

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



You asked:

Evaluate the expression: \(\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012\)

MathBot Answer:

\[\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012 = \frac{6 \sqrt{10}}{3125} \approx 0.00607157310752328831743787560531\]

\[\begin{aligned}\frac{\sqrt{0.144} \cdot 0.96}{0.72} \cdot 0.012& = \sqrt{\frac{144}{1000}} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\& = \sqrt{\frac{18}{125}} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\& = \frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{1}{\frac{72}{100}} \cdot \frac{12}{1000}\\& = \frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{1}{\frac{18}{25}} \cdot \frac{12}{1000}\\& = \frac{3}{25} \cdot \sqrt{10} \cdot \frac{96}{100} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\& = \frac{288}{25} \cdot \sqrt{10} \cdot \frac{1}{100} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\& = \frac{72}{625} \cdot \sqrt{10} \cdot \frac{25}{18} \cdot \frac{12}{1000}\\& = \frac{4}{25} \cdot \sqrt{10} \cdot \frac{12}{1000}\\& = \frac{48}{25} \cdot \sqrt{10} \cdot \frac{1}{1000}\\& = \frac{6}{3125} \cdot \sqrt{10}\end{aligned}\]

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