Question

$$\sqrt{ \frac{ (216) \frac{ 2 }{ 3 } \times (125)2 }{ (0.04)3 } }$$

Answer

100*sqrt(30)

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\sqrt{\frac{\frac{216\times 2\times 125\times 2}{3}}{0.04\times 3}}\]
Simplify  \(216\times 2\)  to  \(432\).
\[\sqrt{\frac{\frac{432\times 125\times 2}{3}}{0.04\times 3}}\]
Simplify  \(432\times 125\)  to  \(54000\).
\[\sqrt{\frac{\frac{54000\times 2}{3}}{0.04\times 3}}\]
Simplify  \(54000\times 2\)  to  \(108000\).
\[\sqrt{\frac{\frac{108000}{3}}{0.04\times 3}}\]
Simplify  \(\frac{108000}{3}\)  to  \(36000\).
\[\sqrt{\frac{36000}{0.04\times 3}}\]
Simplify  \(0.04\times 3\)  to  \(0.12\).
\[\sqrt{\frac{36000}{0.12}}\]
Simplify  \(\frac{36000}{0.12}\)  to  \(300000\).
\[\sqrt{300000}\]
Simplify  \(\sqrt{300000}\)  to  \(100\sqrt{30}\).
\[100\sqrt{30}\]

Decimal Form: 547.722558