Solve =sqrt{2*16595.84/3*80*3600*3.14*6}

$$= \sqrt { \frac { 2 \times 16595.84 } { 3 \times 80 \times 3600 \times 3.14 \times 6 } }$$

Evaluate

$$\frac{\sqrt{40711670}}{141300}\approx 0.045156191$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{16595.84}{3\times 3.14\times 6\times 40\times 3600}}$$

Multiply 3 and 3.14 to get 9.42.

$$\sqrt{\frac{16595.84}{9.42\times 6\times 40\times 3600}}$$

Multiply 9.42 and 6 to get 56.52.

$$\sqrt{\frac{16595.84}{56.52\times 40\times 3600}}$$

Multiply 56.52 and 40 to get 2260.8.

$$\sqrt{\frac{16595.84}{2260.8\times 3600}}$$

Multiply 2260.8 and 3600 to get 8138880.

$$\sqrt{\frac{16595.84}{8138880}}$$

Expand \frac{16595.84}{8138880} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1659584}{813888000}}$$

Reduce the fraction \frac{1659584}{813888000} to lowest terms by extracting and canceling out 64.

$$\sqrt{\frac{25931}{12717000}}$$

Rewrite the square root of the division \sqrt{\frac{25931}{12717000}} as the division of square roots \frac{\sqrt{25931}}{\sqrt{12717000}}.

$$\frac{\sqrt{25931}}{\sqrt{12717000}}$$

Factor 12717000=90^{2}\times 1570. Rewrite the square root of the product \sqrt{90^{2}\times 1570} as the product of square roots \sqrt{90^{2}}\sqrt{1570}. Take the square root of 90^{2}.

$$\frac{\sqrt{25931}}{90\sqrt{1570}}$$

Rationalize the denominator of \frac{\sqrt{25931}}{90\sqrt{1570}} by multiplying numerator and denominator by \sqrt{1570}.

$$\frac{\sqrt{25931}\sqrt{1570}}{90\left(\sqrt{1570}\right)^{2}}$$

The square of \sqrt{1570} is 1570.

$$\frac{\sqrt{25931}\sqrt{1570}}{90\times 1570}$$

To multiply \sqrt{25931} and \sqrt{1570}, multiply the numbers under the square root.

$$\frac{\sqrt{40711670}}{90\times 1570}$$

Multiply 90 and 1570 to get 141300.

$$\frac{\sqrt{40711670}}{141300}$$