\(\sqrt[]{\frac{44.1\cdot \left(3.2\right)^{2}}{8.99\cdot 10^{9}}}\)

asked by guest
on Nov 28, 2024 at 7:43 am



You asked:

Evaluate the expression: \(\sqrt{\frac{44.1 \cdot {3.2}^{2}}{8.99 \cdot {10}^{9}}}\)

MathBot Answer:

\[\sqrt{\frac{44.1 \cdot {3.2}^{2}}{8.99 \cdot {10}^{9}}} = \frac{21 \sqrt{899}}{2809375} \approx 0.00022412454824426354414334505577\]

\[\begin{aligned}\sqrt{\frac{44.1 \cdot {3.2}^{2}}{8.99 \cdot {10}^{9}}}& = \sqrt{\left(44 + \frac{1}{10}\right) \cdot \left(3 + \frac{2}{10}\right)^{2} \cdot \frac{1}{\left(8 + \frac{99}{100}\right) \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \left(3 + \frac{2}{10}\right)^{2} \cdot \frac{1}{\left(8 + \frac{99}{100}\right) \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \left(3 + \frac{1}{5}\right)^{2} \cdot \frac{1}{\left(8 + \frac{99}{100}\right) \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \left(\frac{16}{5}\right)^{2} \cdot \frac{1}{\left(8 + \frac{99}{100}\right) \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \frac{256}{25} \cdot \frac{1}{\left(8 + \frac{99}{100}\right) \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \frac{256}{25} \cdot \frac{1}{\frac{899}{100} \cdot 10^{9}}}\\& = \sqrt{\frac{441}{10} \cdot \frac{256}{25} \cdot \frac{1}{\frac{899}{100} \cdot 1000000000}}\\& = \sqrt{\frac{441}{10} \cdot \frac{256}{25} \cdot \frac{1}{8990000000}}\\& = \sqrt{\frac{441}{10} \cdot \frac{2}{1755859375}}\\& = \sqrt{\frac{441}{8779296875}}\\& = \frac{21}{2809375} \cdot \sqrt{899}\end{aligned}\]

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