Solve sqrt{frac{9*9.806/0.0254*58}}{2*3.14/60}

$$\frac{ \sqrt{ \frac{ 9 \cdot 9.806 }{ 0.0254 \cdot 58 } } }{ \frac{ 2 \cdot 3.14 }{ 60 } }$$

Evaluate

$$\frac{4500\sqrt{90288745}}{578231}\approx 73.948258503$$

Solution Steps

Multiply 9 and 9.806 to get 88.254.

$$\frac{\sqrt{\frac{88.254}{0.0254\times 58}}}{\frac{2\times 3.14}{60}}$$

Multiply 0.0254 and 58 to get 1.4732.

$$\frac{\sqrt{\frac{88.254}{1.4732}}}{\frac{2\times 3.14}{60}}$$

Expand \frac{88.254}{1.4732} by multiplying both numerator and the denominator by 10000.

$$\frac{\sqrt{\frac{882540}{14732}}}{\frac{2\times 3.14}{60}}$$

Reduce the fraction \frac{882540}{14732} to lowest terms by extracting and canceling out 4.

$$\frac{\sqrt{\frac{220635}{3683}}}{\frac{2\times 3.14}{60}}$$

Rewrite the square root of the division \sqrt{\frac{220635}{3683}} as the division of square roots \frac{\sqrt{220635}}{\sqrt{3683}}.

$$\frac{\frac{\sqrt{220635}}{\sqrt{3683}}}{\frac{2\times 3.14}{60}}$$

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}.

$$\frac{\frac{3\sqrt{24515}}{\sqrt{3683}}}{\frac{2\times 3.14}{60}}$$

Rationalize the denominator of \frac{3\sqrt{24515}}{\sqrt{3683}} by multiplying numerator and denominator by \sqrt{3683}.

$$\frac{\frac{3\sqrt{24515}\sqrt{3683}}{\left(\sqrt{3683}\right)^{2}}}{\frac{2\times 3.14}{60}}$$

The square of \sqrt{3683} is 3683.

$$\frac{\frac{3\sqrt{24515}\sqrt{3683}}{3683}}{\frac{2\times 3.14}{60}}$$

To multiply \sqrt{24515} and \sqrt{3683}, multiply the numbers under the square root.

$$\frac{\frac{3\sqrt{90288745}}{3683}}{\frac{2\times 3.14}{60}}$$

Multiply 2 and 3.14 to get 6.28.

$$\frac{\frac{3\sqrt{90288745}}{3683}}{\frac{6.28}{60}}$$

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

$$\frac{\frac{3\sqrt{90288745}}{3683}}{\frac{628}{6000}}$$

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

$$\frac{\frac{3\sqrt{90288745}}{3683}}{\frac{157}{1500}}$$

Divide \frac{3\sqrt{90288745}}{3683} by \frac{157}{1500} by multiplying \frac{3\sqrt{90288745}}{3683} by the reciprocal of \frac{157}{1500}.

$$\frac{3\sqrt{90288745}\times 1500}{3683\times 157}$$

Multiply 3 and 1500 to get 4500.

$$\frac{4500\sqrt{90288745}}{3683\times 157}$$

Multiply 3683 and 157 to get 578231.

$$\frac{4500\sqrt{90288745}}{578231}$$