Math Problem Solver

$$\sqrt{22.5 \cdot 88.86 \cdot 247.51} = \frac{3 \sqrt{549843465}}{100} \approx 703.46223672632207613804036647286827$$

$$\begin{aligned}\sqrt{22.5 \cdot 88.86 \cdot 247.51}&=\sqrt{\left(22 + \frac{5}{10}\right) \cdot \left(88 + \frac{86}{100}\right) \cdot \left(247 + \frac{51}{100}\right)}\\&=\sqrt{\left(22 + \frac{1}{2}\right) \cdot \left(88 + \frac{86}{100}\right) \cdot \left(247 + \frac{51}{100}\right)}\\&=\sqrt{\frac{45}{2} \cdot \left(88 + \frac{86}{100}\right) \cdot \left(247 + \frac{51}{100}\right)}\\&=\sqrt{\frac{45}{2} \cdot \left(88 + \frac{43}{50}\right) \cdot \left(247 + \frac{51}{100}\right)}\\&=\sqrt{\frac{45}{2} \cdot \frac{4443}{50} \cdot \left(247 + \frac{51}{100}\right)}\\&=\sqrt{\frac{45}{2} \cdot \frac{4443}{50} \cdot \frac{24751}{100}}\\&=\sqrt{\frac{39987}{20} \cdot \frac{24751}{100}}\\&=\sqrt{\frac{989718237}{2000}}\\&=\frac{3}{100} \cdot \sqrt{549843465}\end{aligned}$$