Solve sqrt{frac{9*9.806/0.0254*61}}{2*3.14/60}

$$\frac{ \sqrt{ \frac{ 9 \cdot 9.806 }{ 0.0254 \cdot 61 } } }{ \frac{ 2 \cdot 3.14 }{ 60 } }$$

Evaluate

$$\frac{4500\sqrt{379835410}}{1216279}\approx 72.106934055$$

Solution Steps

Multiply 9 and 9.806 to get 88.254.

$$\frac{\sqrt{\frac{88.254}{0.0254\times 61}}}{\frac{2\times 3.14}{60}}$$

Multiply 0.0254 and 61 to get 1.5494.

$$\frac{\sqrt{\frac{88.254}{1.5494}}}{\frac{2\times 3.14}{60}}$$

Expand \frac{88.254}{1.5494} by multiplying both numerator and the denominator by 10000.

$$\frac{\sqrt{\frac{882540}{15494}}}{\frac{2\times 3.14}{60}}$$

Reduce the fraction \frac{882540}{15494} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{\frac{441270}{7747}}}{\frac{2\times 3.14}{60}}$$

Rewrite the square root of the division \sqrt{\frac{441270}{7747}} as the division of square roots \frac{\sqrt{441270}}{\sqrt{7747}}.

$$\frac{\frac{\sqrt{441270}}{\sqrt{7747}}}{\frac{2\times 3.14}{60}}$$

Factor 441270=3^{2}\times 49030. Rewrite the square root of the product \sqrt{3^{2}\times 49030} as the product of square roots \sqrt{3^{2}}\sqrt{49030}. Take the square root of 3^{2}.

$$\frac{\frac{3\sqrt{49030}}{\sqrt{7747}}}{\frac{2\times 3.14}{60}}$$

Rationalize the denominator of \frac{3\sqrt{49030}}{\sqrt{7747}} by multiplying numerator and denominator by \sqrt{7747}.

$$\frac{\frac{3\sqrt{49030}\sqrt{7747}}{\left(\sqrt{7747}\right)^{2}}}{\frac{2\times 3.14}{60}}$$

The square of \sqrt{7747} is 7747.

$$\frac{\frac{3\sqrt{49030}\sqrt{7747}}{7747}}{\frac{2\times 3.14}{60}}$$

To multiply \sqrt{49030} and \sqrt{7747}, multiply the numbers under the square root.

$$\frac{\frac{3\sqrt{379835410}}{7747}}{\frac{2\times 3.14}{60}}$$

Multiply 2 and 3.14 to get 6.28.

$$\frac{\frac{3\sqrt{379835410}}{7747}}{\frac{6.28}{60}}$$

Expand \frac{6.28}{60} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{3\sqrt{379835410}}{7747}}{\frac{628}{6000}}$$

Reduce the fraction \frac{628}{6000} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3\sqrt{379835410}}{7747}}{\frac{157}{1500}}$$

Divide \frac{3\sqrt{379835410}}{7747} by \frac{157}{1500} by multiplying \frac{3\sqrt{379835410}}{7747} by the reciprocal of \frac{157}{1500}.

$$\frac{3\sqrt{379835410}\times 1500}{7747\times 157}$$

Multiply 3 and 1500 to get 4500.

$$\frac{4500\sqrt{379835410}}{7747\times 157}$$

Multiply 7747 and 157 to get 1216279.

$$\frac{4500\sqrt{379835410}}{1216279}$$