44.1⋅(3.2)28.99⋅109\sqrt[]{\frac{44.1\cdot \left(3.2\right)^{2}}{8.99\cdot 10^{9}}}

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on Nov 28, 2024 at 7:43 am



You asked:

Evaluate the expression: 44.1⋅3.228.99⋅109\sqrt{\frac{44.1 \cdot {3.2}^{2}}{8.99 \cdot {10}^{9}}}

MathBot Answer:

44.1⋅3.228.99⋅109=218992809375≈0.00022412454824426354414334505577\sqrt{\frac{44.1 \cdot {3.2}^{2}}{8.99 \cdot {10}^{9}}} = \frac{21 \sqrt{899}}{2809375} \approx 0.00022412454824426354414334505577

44.1⋅3.228.99⋅109=(44+110)⋅(3+210)2⋅1(8+99100)⋅109=44110⋅(3+210)2⋅1(8+99100)⋅109=44110⋅(3+15)2⋅1(8+99100)⋅109=44110⋅(165)2⋅1(8+99100)⋅109=44110⋅25625⋅1(8+99100)⋅109=44110⋅25625⋅1899100⋅109=44110⋅25625⋅1899100⋅1000000000=44110⋅25625⋅18990000000=44110⋅21755859375=4418779296875=212809375⋅899\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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