Solve sqrt{frac{9*9.806/0.0254*64}}{2*3.14/60}

$$\frac{ \sqrt{ \frac{ 9 \cdot 9.806 }{ 0.0254 \cdot 64 } } }{ \frac{ 2 \cdot 3.14 }{ 60 } }$$

Evaluate

$$\frac{1125\sqrt{6226810}}{39878}\approx 70.396644792$$

Solution Steps

Multiply 9 and 9.806 to get 88.254.

$$\frac{\sqrt{\frac{88.254}{0.0254\times 64}}}{\frac{2\times 3.14}{60}}$$

Multiply 0.0254 and 64 to get 1.6256.

$$\frac{\sqrt{\frac{88.254}{1.6256}}}{\frac{2\times 3.14}{60}}$$

Expand \frac{88.254}{1.6256} by multiplying both numerator and the denominator by 10000.

$$\frac{\sqrt{\frac{882540}{16256}}}{\frac{2\times 3.14}{60}}$$

Reduce the fraction \frac{882540}{16256} to lowest terms by extracting and canceling out 4.

$$\frac{\sqrt{\frac{220635}{4064}}}{\frac{2\times 3.14}{60}}$$

Rewrite the square root of the division \sqrt{\frac{220635}{4064}} as the division of square roots \frac{\sqrt{220635}}{\sqrt{4064}}.

$$\frac{\frac{\sqrt{220635}}{\sqrt{4064}}}{\frac{2\times 3.14}{60}}$$

Factor 220635=3^{2}\times 24515. Rewrite the square root of the product \sqrt{3^{2}\times 24515} as the product of square roots \sqrt{3^{2}}\sqrt{24515}. Take the square root of 3^{2}.

$$\frac{\frac{3\sqrt{24515}}{\sqrt{4064}}}{\frac{2\times 3.14}{60}}$$

Factor 4064=4^{2}\times 254. Rewrite the square root of the product \sqrt{4^{2}\times 254} as the product of square roots \sqrt{4^{2}}\sqrt{254}. Take the square root of 4^{2}.

$$\frac{\frac{3\sqrt{24515}}{4\sqrt{254}}}{\frac{2\times 3.14}{60}}$$

Rationalize the denominator of \frac{3\sqrt{24515}}{4\sqrt{254}} by multiplying numerator and denominator by \sqrt{254}.

$$\frac{\frac{3\sqrt{24515}\sqrt{254}}{4\left(\sqrt{254}\right)^{2}}}{\frac{2\times 3.14}{60}}$$

The square of \sqrt{254} is 254.

$$\frac{\frac{3\sqrt{24515}\sqrt{254}}{4\times 254}}{\frac{2\times 3.14}{60}}$$

To multiply \sqrt{24515} and \sqrt{254}, multiply the numbers under the square root.

$$\frac{\frac{3\sqrt{6226810}}{4\times 254}}{\frac{2\times 3.14}{60}}$$

Multiply 4 and 254 to get 1016.

$$\frac{\frac{3\sqrt{6226810}}{1016}}{\frac{2\times 3.14}{60}}$$

Multiply 2 and 3.14 to get 6.28.

$$\frac{\frac{3\sqrt{6226810}}{1016}}{\frac{6.28}{60}}$$

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

$$\frac{\frac{3\sqrt{6226810}}{1016}}{\frac{628}{6000}}$$

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

$$\frac{\frac{3\sqrt{6226810}}{1016}}{\frac{157}{1500}}$$

Divide \frac{3\sqrt{6226810}}{1016} by \frac{157}{1500} by multiplying \frac{3\sqrt{6226810}}{1016} by the reciprocal of \frac{157}{1500}.

$$\frac{3\sqrt{6226810}\times 1500}{1016\times 157}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3\times 375\sqrt{6226810}}{157\times 254}$$

Multiply 3 and 375 to get 1125.

$$\frac{1125\sqrt{6226810}}{157\times 254}$$

Multiply 157 and 254 to get 39878.

$$\frac{1125\sqrt{6226810}}{39878}$$