1/√(0.1 ×10^(-3) ×0.22 ×10^(-6) )

asked by guest
on Mar 17, 2025 at 4:33 am



You asked:

Evaluate the expression: 10.1⋅10−3⋅0.22⋅10−6\frac{1}{\sqrt{0.1 \cdot {10}^{-3} \cdot 0.22 \cdot {10}^{-6}}}

MathBot Answer:

10.1⋅10−3⋅0.22⋅10−6=5000002211≈213200.71635561043429843773243383937639\frac{1}{\sqrt{0.1 \cdot {10}^{-3} \cdot 0.22 \cdot {10}^{-6}}} = \frac{500000 \sqrt{22}}{11} \approx 213200.71635561043429843773243383937639

10.1⋅10−3⋅0.22⋅10−6=1110⋅1103⋅22100⋅1106=1110⋅221000⋅1100⋅1106=1110⋅221000⋅1100⋅11000000=12210000⋅1100⋅11000000=1115000⋅1100⋅11000000=111500000⋅11000000=111500000000000=111000000⋅22=50000011⋅22\begin{aligned}\frac{1}{\sqrt{0.1 \cdot {10}^{-3} \cdot 0.22 \cdot {10}^{-6}}}&=\frac{1}{\sqrt{\frac{1}{10} \cdot \frac{1}{10^{3}} \cdot \frac{22}{100} \cdot \frac{1}{10^{6}}}}\\&=\frac{1}{\sqrt{\frac{1}{10} \cdot \frac{22}{1000} \cdot \frac{1}{100} \cdot \frac{1}{10^{6}}}}\\&=\frac{1}{\sqrt{\frac{1}{10} \cdot \frac{22}{1000} \cdot \frac{1}{100} \cdot \frac{1}{1000000}}}\\&=\frac{1}{\sqrt{\frac{22}{10000} \cdot \frac{1}{100} \cdot \frac{1}{1000000}}}\\&=\frac{1}{\sqrt{\frac{11}{5000} \cdot \frac{1}{100} \cdot \frac{1}{1000000}}}\\&=\frac{1}{\sqrt{\frac{11}{500000} \cdot \frac{1}{1000000}}}\\&=\frac{1}{\sqrt{\frac{11}{500000000000}}}\\&=\frac{1}{\frac{1}{1000000} \cdot \sqrt{22}}\\&=\frac{500000}{11} \cdot \sqrt{22}\end{aligned}

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