Math Problem Solver

$$2.575 \cdot \frac{7.4}{\sqrt{463}} = \frac{3811 \sqrt{463}}{92600} \approx 0.88556095021419980061083755774904$$

$$\begin{aligned}2.575 \cdot \frac{7.4}{\sqrt{463}}&=\left(2 + \frac{575}{1000}\right) \cdot \left(7 + \frac{4}{10}\right) \cdot \frac{1}{\sqrt{463}}\\&=\left(2 + \frac{23}{40}\right) \cdot \left(7 + \frac{4}{10}\right) \cdot \frac{1}{\sqrt{463}}\\&=\frac{103}{40} \cdot \left(7 + \frac{4}{10}\right) \cdot \frac{1}{\sqrt{463}}\\&=\frac{103}{40} \cdot \left(7 + \frac{2}{5}\right) \cdot \frac{1}{\sqrt{463}}\\&=\frac{103}{40} \cdot \frac{37}{5} \cdot \frac{1}{\sqrt{463}}\\&=\frac{103}{40} \cdot \frac{37}{2315} \cdot \sqrt{463}\\&=\frac{3811}{92600} \cdot \sqrt{463}\end{aligned}$$