Solve sqrt{2*16595.84/3*3600*66*3.14*10}

$$\sqrt{ \frac{ 2 \cdot 16595.84 }{ 3 \cdot 3600 \cdot 66 \cdot 3.14 \cdot 10 } }$$

Evaluate

$$\frac{\sqrt{223914185}}{388575}\approx 0.038509329$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{16595.84}{3\times 3.14\times 10\times 66\times 1800}}$$

Multiply 3 and 3.14 to get 9.42.

$$\sqrt{\frac{16595.84}{9.42\times 10\times 66\times 1800}}$$

Multiply 9.42 and 10 to get 94.2.

$$\sqrt{\frac{16595.84}{94.2\times 66\times 1800}}$$

Multiply 94.2 and 66 to get 6217.2.

$$\sqrt{\frac{16595.84}{6217.2\times 1800}}$$

Multiply 6217.2 and 1800 to get 11190960.

$$\sqrt{\frac{16595.84}{11190960}}$$

Expand \frac{16595.84}{11190960} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1659584}{1119096000}}$$

Reduce the fraction \frac{1659584}{1119096000} to lowest terms by extracting and canceling out 64.

$$\sqrt{\frac{25931}{17485875}}$$

Rewrite the square root of the division \sqrt{\frac{25931}{17485875}} as the division of square roots \frac{\sqrt{25931}}{\sqrt{17485875}}.

$$\frac{\sqrt{25931}}{\sqrt{17485875}}$$

Factor 17485875=45^{2}\times 8635. Rewrite the square root of the product \sqrt{45^{2}\times 8635} as the product of square roots \sqrt{45^{2}}\sqrt{8635}. Take the square root of 45^{2}.

$$\frac{\sqrt{25931}}{45\sqrt{8635}}$$

Rationalize the denominator of \frac{\sqrt{25931}}{45\sqrt{8635}} by multiplying numerator and denominator by \sqrt{8635}.

$$\frac{\sqrt{25931}\sqrt{8635}}{45\left(\sqrt{8635}\right)^{2}}$$

The square of \sqrt{8635} is 8635.

$$\frac{\sqrt{25931}\sqrt{8635}}{45\times 8635}$$

To multiply \sqrt{25931} and \sqrt{8635}, multiply the numbers under the square root.

$$\frac{\sqrt{223914185}}{45\times 8635}$$

Multiply 45 and 8635 to get 388575.

$$\frac{\sqrt{223914185}}{388575}$$