$\sqrt{\22.5*88.86*247.51}$

asked by guest
on Jan 09, 2025 at 10:08 am



You asked:

Evaluate the expression: \(\sqrt{22.5 \cdot 88.86 \cdot 247.51}\)

MathBot Answer:

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

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

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